## Exam (elaborations)

# Rasmussen College - MATH STA 3215 Math Pre Test ONE

MATH STA 3215 Pretest Module 01 What can be the minimum integer value of 'a' for Player 1 to have a strictly dominant strategy? Select the correct option. Select one: a. 2 b. 3 c. 4 d. 5 Question 2 In the game shown below, the numbers in the cells show payoffs to Players 1 and 2. What is Player 1's dominant strategy? Select the correct option. Select one: a. A is the dominant strategy b. B is the dominant strategy c. Player 1 does not have a dominant strategy d. Both A and B are dominant strategies Question 3 A game matrix is shown below: Choose the correct statement among the following: Select the correct option. Select one: a. Both players have a dominant strategy b. Run is the dominant strategy for Bob c. (Run, Run) is the Nash equilibrium d. If Bob chooses Run, Alice’s best response is Run Question 4 For the game shown below, choose from the options the acceptable integer values of 'x' and 'y' for both players to have strictly dominant strategies. Select the correct option. Select one: a. x=3, y=2 b. x=2, y=2 c. x =2, y=3 d. x=3, y=3 Question 5 What can be the minimum integer value of 'a' for Player 1 to have a strictly dominant strategy? Select the correct option. Select one: a. 2 b. 3 c. 4 d. 5 Question 6 In the game shown below, the numbers in the cells show payoffs to Players 1 and 2. What is player 1's dominant strategy? Select the correct option. Select one: a. A is the dominant strategy b. B is the dominant strategy c. Player 1 does not have a dominant strategy d. Both A and B are dominant strategies Question 7 For the game shown below, choose from the options the acceptable integer values of 'x' and 'y' for both players to have strictly dominant strategies Select the correct option. Select one: a. x=4, y=2 b. x=5, y=1 c. x=3, y=4 d. x=2, y=3 Question 8 In the following game, the payoffs are ranks of the outcomes for each player with 1 being the best and 4 being the worst. Identify the correct statement from the options. Select the correct option. Select one: a. Player 1 has a strictly dominant strategy: A b. Player 2 has a strictly dominant strategy: C c. Both B and C are strictly dominant strategies d. Both A and C are strictly dominant strategies Question 9 For the game shown below, identify the correct statement from the given options Select the correct option. Select one: a. If Player 1 chooses A, Player 2’s best response is E b. If player 2 chooses F Player 1’s best response is C c. If Player 1 chooses C, Player 2’s best response is E d. If Player 2 chooses D, Player 1’s best response is A Question 10 For the game shown below, identify the correct statement from the given options Select the correct option. Select one: a. If Player 2 chooses F, Player 1’s best response is B b. If player 2 chooses E Player 1’s best response is B c. If Player 1 chooses C, Player 2’s best response is E d. If Player 1 chooses A, Player 2’s best response is E Pretest Module 02 A game matrix is shown below: Choose the correct statement among the following: Select the correct option. Select one: a. Both players have a dominant strategy b. Run is the dominant strategy for Bob c. (Run, Run) is the Nash equilibrium d. If Bob chooses Run, Alice’s best response is Run Question 2 For the game shown below, identify the mixed strategy Nash equilibrium where 'p' is the probability that Bob chooses A and 'q' is the probability that Mary chooses C Select the correct option. Select one: a. (p=2/3, q=2/3) b. (p=1/3, q=1/3) c. (p=1/2, q=1/2) d. (p=1/3, q=2/3) Question 3 Rachel buys a new CD, on which is her favourite track, 8 other tracks she likes and 2 tracks that she does not like. She sets her CD player to play at random.What is the probability that the first track it plays is a track she just likes? Select the correct option. Select one: a. 1/11 b. 9/11 c. 8/11 d. 2/11 Question 4 A coin is flipped 3 times. What is the probability of getting two tails and one head? Select the correct option. Select one: a. 1/2 b. 1/8 c. 3/8 d. 1/4 Question 5 There are 18 boys and 17 girls in a class.One of these students is selected at random to represent the class. What is the probability that the student selected is a girl? Select the correct option. Select one: a. 1/35 b. 1/17 c. 18/35 d. 17/35 Question 6 Bob randomly picks a number from 1 to 6 (both inclusive). What is the probability that he picks a number more than 3? Select the correct option. Select one: a. 0.5 b. 0.4 c. 0.3 d. 0.2 Question 7 A prisoners' dilemma is a game with all of the following characteristics except one. Choose the characteristic that is not applicable to a prisoners' dilemma game Select the correct option. Select one: a. Both players have a dominant strategy b. Both players would get higher payoffs if none of them chose the dominant strategy c. The payoff from one player’s strategy depends on the choice by the other player d. Players cooperate and select their strategies Question 8 John randomly picks a number from 1 to 5 (both inclusive) and a letter from A to E (both inclusive). What is the probability that he picks 2 and E? Select the correct option. Select one: a. 1/25 b. 1/30 c. 1/4 d. 1/5 Question 9 John writes a computer program that produces at random one of these digits:0, 1, 2, 3, 4, 5, 6, 7, 8, 9. What is the probability that the program produces a multiple of 4? Select the correct option. Select one: a. 3/10 b. 1/5 c. ½ d. 1/10 Question 10 For the game shown below, identify the mixed strategy Nash equilibrium where 'p' is the probability that Bob chooses A and 'q' is the probability that Mary chooses C Select the correct option. Select one: a. (p=2/3, q=2/3) b. (p=1/3, q=1/3) c. (p=1/2, q=1/2) d. (p=1/3, q=2/3) Test Module 01 Question 1 Alice rolls two dice. What is the probability of rolling two 6s? Select the correct option. Select one: a. 1/6 b. 1/12 c. 1/36 d. 1/18 Question 2 John randomly picks a number from 1 to 5 (both inclusive) and a letter from A to E (both inclusive). What is the probability that he picks 2 and E? Select the correct option. Select one: a. 1/25 b. 1/30 c. 1/4 d. 1/5 Question 3 A fair dice is tossed 6 times. Find the probability of getting a third six on the sixth throw. Select the correct option. Select one: a. 5C2 x 52 / 66 b. 5C2 x 53 / 66 c. 5C2 x 54 / 66 d. 5C3 x 52 / 66 Question 4 A box contains 4 red pencils and 5 blue pencils. 4 pencils are taken out one after the other without replacement. What is the probability that the pencils drawn are red, blue, blue and red in that order (approximated to two decimal places)? Select the correct option. Select one: a. 0.06 b. 0.07 c. 0.08 d. 0.09 Question 5 A bag contains 3 white and 5 black balls. Bob draws two balls one after another from the bag, without replacement. What is the probability that any one ball is white and the other is black? Select the correct option. Select one: a. 25/56 b. 15/28 c. 15/56 d. 45/56 Question 6 Bob randomly picks a number from 1 to 6 (both inclusive). What is the probability that he picks a number more than 3? Select the correct option. Select one: a. 0.5 b. 0.4 c. 0.3 d. 0.2 Question 7 For the game shown below, identify the mixed strategy Nash equilibrium where 'p' is the probability that Bob chooses A and 'q' is the probability that Mary chooses C Select the correct option. Select one: a. (p=2/3, q=2/3) b. (p=1/3, q=1/3) c. (p=1/2, q=1/2) d. (p=1/3, q=2/3) Question 8 If the probability of an event to occur is 0.4. What is the probability that the event will not occur? Select the correct option. Select one: a. 0.5 b. 0.4 c. 0.6 d. 0.7 Question 9 A pair of dice is rolled till a sum of either 5 or 7 is obtained. The probability that 5 comes before 7 is : Select the correct option. Select one: a. 0.45 b. 0.4 c. 0.5 d. 0.6 Question 10 A die is rolled. What is the probability of rolling an even number? Select the correct option. Select one: a. 1/4 b. 1/2 c. 2/3 d. 1/6 Question 11 A group of children has 2 boys and 2 girls. 2 children are selected from the group. What is the probability that a boy and a girl get selected? Select the correct option. Select one: a. 1/6 b. 2/3 c. 1/2 d. 1 /4 Question 12 Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even ? Select the correct option. Select one: a. 3/4 b. 1/4 c. 11/12 d. 1/2 Question 13 When two dice are thrown simultaneously, what is the probability that the sum of the two numbers that turn up is less than 11? Select the correct option. Select one: a. 5/6 b. 11/12 c. 1/6 d. 1/12 Question 14 If the probability that an event occurs is 'p' and the probability that the event does not occur is 'q', which of the following is necessarily true? Select the correct option. Select one: a. (p q)(p-q)=1 b. P^2 q^2=1 c. p-q>0 d. p(1-q) q(1-p) 2(1-p)(1-q)=1 Question 15 A game matrix is shown below: Choose the correct statement among the following: Select the correct option. Select one: a. Both players have a dominant strategy b. Run is the dominant strategy for Bob c. (Run, Run) is the Nash equilibrium d. If Bob chooses Run, Alice’s best response is Run Question 16 A coin is tossed once. What is the probability of getting heads or tails? Select the correct option. Select one: a. 0 b. 0.25 c. 1 d. 0.5 Question 17 A bag contains 3 white and 5 black balls. Alice draws two balls one after another from the bag, without replacement. What is the probability that the first ball is white and the second black? Select the correct option. Select one: a. 2/28 b. 15/56 c. 12/36 d. 15/64 Question 18 For the game shown below, identify the mixed strategy Nash equilibrium where 'p' is the probability that Bob chooses A and 'q' is the probability that Mary chooses C Select the correct option. Select one: a. (p=2/3, q=2/3) b. (p=1/3, q=1/3) c. (p=1/2, q=1/2) d. (p=1/3, q=2/3) Question 19 Alice rolls two dice. What is the probability of obtaining at least one 6? Select the correct option. Select one: a. 1/6 b. 1/24 c. 10/36 d. 11/36 Question 20 A prisoners' dilemma is a game with all of the following characteristics except one. Choose the characteristic that is not applicable to a prisoners' dilemma game Select the correct option. Select one: a. Both players have a dominant strategy b. Both players would get higher payoffs if none of them chose the dominant strategy c. The payoff from one player’s strategy depends on the choice by the other player d. Players cooperate and select their strategies Pretest Module 3 A coin is tossed and if it lands heads you will get 100 dollars. If the coin lands tails you will be paid 50 dollars. What is the expected value of this toss? Select the correct option. Select one: a. 50 b. 75 c. 100 d. 25 Question 2 How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, if digits can only be used once? Select the correct option. Select one: a. 216 b. 20 c. 6 d. 120 Question 3 How many four letter distinct initials can be formed using the alphabets of English language such that the last of the four words is always a consonant? Select the correct option. Select one: a. (263)*(21) b. 26*25*24*21 c. 25*24*23*21 d. 25*24*23*22 Question 4 What is the probability that after reshuffling, the four S's come consecutively in the word MISSISSIPPI? Select the correct option. Select one: a. 4/165 b. 2/165 c. 3/165 d. 1/165 Question 5 In a game between two teams A and B, John is set to win 200 dollars if A wins, and 100 dollars if B wins. John calculates his expected winning to be 170 dollars. According to John's calculations, what is the probability that B wins (given no probability of a tied/drawn game)? HINT: Let the probability that B wins be P, and which means the probabilty that A wins is (1 - P) and then set up the expected value accordingly and solve for P. Select the correct option. Select one: a. 0.3 b. 0.5 c. 0.4 d. 0.7 Question 6 There are 6 boxes numbered 1, 2, ... 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is: Select the correct option. Select one: a. 5 b. 21 c. 33 d. 60 Question 7 In a factory, the probability that a manufactured item is defective is 20%. In a lot of 200 items, what is the expected number of defective items? Select the correct option. Select one: a. 30 b. 40 c. 20 d. 50 Question 8 A fair die is rolled and Rob is offered the dollar value of the number that shows up. What is Rob's expected payoff? Select the correct option. Select one: a. 5.5 b. 4.5 c. 3.5 d. 2.5 Question 9 Out of 10 consecutive integers, two are chosen at random. Find the probability that their sum is odd. Select the correct option. Select one: a. 1/2 b. 20/39 c. 19/39 d. 19/40 Question 10 From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done? Select the correct option. Select one: a. 564 b. 645 c. 735 d. 756 Pretest Module 04 Question 1 Calculate the pure strategy equilibrium of the game shown below where the payoffs to Bob have been mentioned Select the correct option. Select one: a. (B,D) b. (A,E) c. (C,D) d. (A,F) Question 2 Calculate the mixed strategy equilibrium of the game shown below Select the correct option. Select one: a. P(A)=1/2, P(C)=1/2 b. P(A)=3/8, P(C)=4/9 c. P(A)=2/5, P(C)=1/7 d. P(A)=4/7, P(C)=4/7 Question 3 Calculate the pure strategy equilibrium of the game shown below where the payoffs to John have been mentioned Select the correct option. Select one: a. (B,E) b. (C,E) c. (C,D) d. (A,F) Question 4 Calculate the pure strategy equilibrium of the game shown below where the payoffs to Bob have been mentioned Select the correct option. Select one: a. No pure strategy equilibrium b. (Chase, Walk) c. (Stop, Chase) d. (Chase, Chase) Question 5 Calculate the mixed strategy equilibrium of the game shown below Select the correct option. Select one: a. P(A)=1/4, P(C)=1/4 b. P(A)=1/3, P(C)=1/3 c. P(A)=1/2, P(C)=1/2 d. P(A)=2/5, P(C)=1/5 Question 6 Calculate the mixed strategy equilibrium of the game shown below Select the correct option. Select one: a. P(A)=1/2, P(C)=1/2 b. P(A)=3/8, P(C)=4/9 c. P(A)=2/5, P(C)=1/7 d. P(A)=4/7, P(C)=4/7 Question 7 Calculate the mixed strategy equilibrium of the game shown below Select the correct option. Select one: a. P(A)=2/5, P(C)=2/5 b. P(A)=1/5, P(C)=1/5 c. P(A)=2/3, P(C)=2/3 d. P(A)=2/5, P(C)=1/5 Question 8 Calculate the mixed strategy equilibrium of the game shown below Select the correct option. Select one: a. P(A)=3/7, P(C)=2/5 b. P(A)=4/9, P(C)=4/9 c. P(A)=4/7, P(C)=4/7 d. P(A)=2/5, P(C)=1/5 Question 9 Calculate the pure strategy equilibrium of the game shown below using Minimax method (4, -4) (-3,3) (-3,3) (2,-2) Select the correct option. Select one: a. (A,C) b. (A,D) c. (B,C) d. No pure strategy equilibrium Question 10 Calculate the pure strategy equilibrium of the game shown below using Minimax method (3,-3) (3,-3) Select the correct option. Select one: a. (A,C) b. (B,C) c. (B,D) d. No pure strategy equilibrium Pretest Module 05 Question 1 A game between two players is shown below The payoffs for players 1 and 2 at equilibria (in pure strategies) are Select the correct option. Select one: a. (1,2), (3,1) b. (2,3), (2,3) c. (3,1) d. (1,2) and (2,1) Question 2 A game between two players is shown below The payoffs for players 1 and 2 at equilibria (in pure strategies) are Select the correct option. Select one: a. (7,6) b. (8,5) c. (6,4) d. (6,7) Question 3 Identify the zero sum game from the following D. (11, -11) (-4,4) (-22, 22) (1, -1) Select the correct option. Select one: a. b. c. d. Question 4 Identify the correct statement among the options given below Select the correct option. Select one: a. In a zero sum game, the payoffs to both players are always positive b. Zero sum games are always competitive c. Non Zero sum games have higher payoffs than zero sum games d. Zero sum games do not have Nash Equilibria Question 5 Identify the correct statement from the following Select the correct option. Select one: a. Zero sum games always have a pure strategy Nash Equilibrium b. Non-Zero Sum games do not have negative payoffs to any player c. Zero sum games always have an equilibrium if players are allowed to have a mixed strategy d. Zero sum games can only be solved by the minimax method Question 6 Identify the zero sum game from the following C. (-4, 4) (-5, 5) (-3, 3) (-1, 1) Select the correct option. Select one: a. b. c. d. Question 7 Identify the correct example of a zero sum game from the following Select the correct option. Select one: a. Prisoner's dilemma b. Game of Chicken c. Rock-Paper-Scissors d. Stag hunt Question 8 A game between two players is shown below The payoffs for players 1 and 2 at equilibria (in pure strategies) are Select the correct option. Select one: a. (2,1), (2,3) b. (3,4), (3,1) c. (3,4) and (3,3) d. (2,3) and (3,3) Question 9 A game between two players is shown below The payoffs for players 1 and 2 at equilibria (in pure and mixed strategies) are Select the correct option. Select one: a. (5,5), (5,5) and (1.5, 1.5) b. (5,5), (5,5) and (3.3, 3.3) c. (2,1), (1,2) and (2.5, 2.5) d. (2,1), (1,2) and (0.5, 0.5) Question 10 In an industry two firms A and B have net annual profits of $30 million each. If A invests in advertising and B does not, then A's net profit will increase to $40 million, and B's will decrease to 10 million. Conversely, if B invests in advertising and A does not, then B's net profit will increase to $40 million and A's will decrease to $ 10 million. However, if both invest in advertising neither A nor B will have any incremental advantage and both the firms will have profits of $20 million. If neither A nor B advertises both continue to have profits of $30 million each. Both A and B decide simultaneously from choices: 'Advertise' and 'Don't Advertise'. What is the Nash Equilibrium of this game? Select the correct option. Select one: a. A advertises, B does not b. B advertises A does not c. Neither A nor B advertises d. Both A and B advertise Pretest Module 06 Question 1 A sequential game is shown below: At equilibrium, choose the correct option from the following Select the correct option. Select one: a. Firm A chooses “Don’t Invest” and B chooses “accommodates” b. Firm A chooses “Invest” and B chooses “Fight” c. The equilibrium payoffs are (2,1) d. This game has no SPE Question 2 Two Firms A and B are playing the following game as shown The numbers are the payoffs for Firm A and B respectively. If A chooses L, B should choose Select the correct option. Select one: a. W b. X c. Y d. Z Question 3 A sequential game is shown below: At equilibrium, choose the correct option from the following Select the correct option. Select one: a. Firm A chooses “Don’t Invest” and B chooses “Fight” b. Firm A chooses “Invest” and B chooses “Fight” c. The equilibrium payoffs are (2,2) d. Firm A chooses “Don’t Invest” and B chooses “Accommodates” Question 4 Two Firms A and B are playing the following game as shown The numbers are the payoffs for Firm A and B respectively. Identify the payoffs to A and B at SPE Select the correct option. Select one: a. (1,2) b. (2,1) c. (2,-1) d. (1,-3) Question 5 Two Firms A and B are playing the following game where A is deciding whether to enter B's market. The numbers are the payoffs for Firm A and B respectively. If B chooses to Fight, Firm A should choose Select the correct option. Select one: a. Fight b. Don’t Fight c. Exit d. Don’t Enter Question 6 A sequential game is shown below: Identify the SPE of the game Select the correct option. Select one: a. ((X,X,M) b. ((Y,Y),L) c. ((Y,Y),M) d. ((Y,X),M) Question 7 Two players Bob and Alice are playing the following game The numbers in the cells are the respective payoffs to the players as per convention If Bob chooses 'Fight' with probability 'p' and Alice chooses 'Fight' with probability 'q', for x=y=10, the mixed strategy equilibrium is Select the correct option. Select one: a. ( p=1/2, q=1/2) b. (p=1/3, q=1/3) c. No mixed strategy equilibrium d. (p=2/3, q=2/3) Question 8 Two Firms A and B are playing the following game where A is deciding whether to enter B’s market. The numbers are the payoffs for Firm A and B respectively. If B accommodates, Firm A should choose Select the correct option. Select one: a. Fight b. Don’t Fight c. Exit d. Don’t Enter Question 9 Two Firms A and B are playing the following game where A is deciding whether to enter B’s market. The numbers are the payoffs for Firm A and B respectively. If A chooses to Enter, Firm B should choose Select the correct option. Select one: a. Fight b. Accommodates c. Exit d. Don’t Enter Question 10 A sequential game is shown below: Identify the SPE of the game Select the correct option. Select one: a. (Don’t Invest, (Accommodate, Accommodate)) b. (Invest, (Accommodate, Fight) c. (Invest, (Accommodate, Accommodate) d. (Don’t Invest, (Fight, Fight)) Test Module 04 Question 1 Calculate the pure strategy equilibrium of the game shown below using Minimax method Select the correct option. Select one: a. (A,C) b. (A,D) c. (B,C) d. No pure strategy equilibrium Question 2 Calculate the pure strategy equilibrium of the game shown below using Minimax method Select the correct option. Select one: a. (A,C) b. (B,C) c. (B,D) d. No pure strategy equilibrium Question 3 Calculate the pure strategy equilibrium of the game shown below where the payoffs to John have been mentioned Select the correct option. Select one: a. (B,E) b. (C,E) c. (C,D) d. (A,F) Question 4 Calculate the pure strategy equilibrium of the game shown below where the payoffs to Bob have been mentioned Select the correct option. Select one: a. (B,D) b. (A,E) c. (C,D) d. (A,F) Question 5 Calculate the pure strategy equilibrium of the game shown below where the payoffs to Bob have been mentioned Select the correct option. Select one: a. No pure strategy equilibrium b. (Chase, Walk) c. (Stop, Chase) d. (Chase, Chase) Question 6 Calculate the mixed strategy equilibrium of the game shown below Select the correct option. Select one: a. P(A)=0.4, P(C)=0.5 b. P(A)=0.5, P(C)=0.5 c. P(A)=0.4, P(C)=0.6 d. P(A)=0.6, P(C)=0.4 Question 7 Calculate the mixed strategy equilibrium of the game shown below Select the correct option. Select one: a. P(A)=0.34, P(C)=0.45 b. P(A)=0.45, P(C)=0.56 c. P(A)=0.24, P(C)=0.36 d. P(A)=0.66, P(C)=0.24 Question 8 Calculate the mixed strategy equilibrium of the game shown below Select the correct option. Select one: a. P(A)=0.27, P(C)=0.54 b. P(A)=0.45, P(C)=0.56 c. P(A)=0.36, P(C)=0.45 d. P(A)=0.66, P(C)=0.24 Question 9 Calculate the mixed strategy equilibrium of the game shown below Select the correct option. Select one: a. P(A)=0.38, P(C)=0.44 b. P(A)=0.54, P(C)=0.25 c. P(A)=0.36, P(C)=0.45 d. P(A)=0.62, P(C)=0.32 Question 10 Calculate the mixed strategy equilibrium of the game shown below Select the correct option. Select one: a. P(A)=0.3, P(C)=0.4 b. P(A)=0.5, P(C)=0.5 c. P(A)=0.6, P(C)=0.4 d. P(A)=0.6, P(C)=0.2 Question 11 Calculate the value of the game shown below Select the correct option. Select one: a. 2 b. -2 c. 3 d. -3 Question 12 Calculate the value of the game shown below Select the correct option. Select one: a. 1 b. -1 c. 2 d. 0 Question 13 For the following game, identify the correct statement Select the correct option. Select one: a. The game is unfair; value=-0.5 b. The game is unfair; value=0.3 c. The game is unfair; value=0.2 d. If payoffs for (B,D) change to (-1, 1) the value does not change Question 14 Calculate the value of the game shown below Select the correct option. Select one: a. 0.5 b. 0.3 c. 0.2 d. 1 Question 15 For the game shown below identify the correct statement Select the correct option. Select one: a. The value of the game is 0 b. If payoffs for (B,C) change to (1,-1), the value of the game is 2.17 c. The value of the game is -0.2 d. If payoffs for (B,C) change to (-2,2) the value of the game is -0.22 Question 16 For the the game shown below, Bob chooses A with probability 'p' and Alice chooses C with probability 'q'. Write the payoff Bob gets by choosing A Select the correct option. Select one: a. p (1-p) b. 1* q-1*(1-q) c. -1*q 1*(1-q) d. –1*p 1*(1-p) Question 17 For the the game shown below, John chooses A with probability 'p' and Stark chooses C with probability 'q'. Write the payoff Stark gets by choosing D Select the correct option. Select one: a. -3*p 3*(1-p) b. 3*p-3*(1-p) c. 2*p-4*(1-p) d. -2*p 3*(1-p) Question 18 For the the game shown below, Tyrion chooses A with probability 'p' and Jamie chooses C with probability 'q'. The lines corresponding to Tyrion's payoffs from choosing A and B respectively intersect at Select the correct option. Select one: a. q=1/2 b. q=1/5 c. q=3/10 d. q=2/5 Question 19 For the the game shown below, Bob chooses A with probability ‘p’ and John chooses C with probability ‘q’. The lines corresponding to John’s payoff from choosing C and D respectively intersect at Select the correct option. Select one: a. p=1/2 b. p=2/5 c. p=3/5 d. p=4/5 Question 20 For the the game shown below, Bill chooses A with probability 'p' and Hillary chooses C with probability 'q'. The lines corresponding to Hillary's payoff from choosing C and D respectively intersect at Select the correct option. Select one: a. p=1/3 b. p=1/4 c. p=1/2 d. q=2/5