OPEN MATH REVIEW FOR EXAM 1
QUESTIONS WITH CORRECT ANSWERS
2.2 Roulette wheel: The game of roulette involves spinning a wheel with 38 slots: 18
red, 18 black, and 2 green. A ball is spun onto the wheel and will eventually land in a
slot, where each slot has an equal chance of capturing the ball.
a) You watch a roulette wheel spin 4 consecutive times and the ball lands on a red slot
each time. What is the probability that the ball will land on a red slot on the next spin?
(please round to four decimal places)
b) You watch a roulette wheel spin 210 consecutive times and the ball lands on a red
slot each time. What is the probability that the ball will land on a red slot on the next
spin? (please round to four decimal places) - Answer a) 18(red)/38(total slots) = .4737
b) 18(red)/38(total slots) = .4737
2.5 Coin Flips: If you flip a fair coin 8 times, what is the probability of each of the
following?(please round all answers to 4 decimal places)
a) getting all tails?
b) getting all heads?
c) getting at least one tails? - Answer a) (1/2)(tails)^8(flips) = 0.0039
b)(1/2)(heads)^8(flips) = 0.0039
c) 1 - (1/2)^8 = 0.9960
2.6 Dice Rolls: If you roll a pair of fair dice, what is the probability of each of the
following? (round all answers to 4 decimal places)
a) getting a sum of 1?
b) getting a sum of 5?
c) getting a sum of 12? - Answer a) 0.0000
minimum = 2
b) 4(combinations)/36(6^2) = 0.1111
,c) 1(combinations)/36(6^2) = 0.0278
2.9 Disjoint vs. independent: In parts (a) and (b), identify whether the events are disjoint,
independent, or neither (events cannot be both disjoint and independent).
a) You and a randomly selected student from your class both earn A's in this course.
b) You and your class partner both earn A's in this course.
c) If two events can occur at the same time, they must be independent. - Answer a)
independent
b) neither
c) false
2.10 Guessing on an exam: In a multiple choice exam, there are 6 questions and 4
choices for each question (a, b, c, d). Nancy has not studied for the exam at all and
decides to randomly guess the answers. What is the probability that:(please round all
answers to four decimal places)
a) the first question she gets right is question number 5?
b) she gets all of the questions right?
c) she gets at least one question right? - Answer a) (3/4)^4*(1/4) = .0791
b) (1/4)^6 = .0002
c) 1-(3/4)^6 = .8220
2.17 Global warming: A research poll asked 1499 Americans "From what you've read
and heard, is there solid evidence that the average temperature on earth has been
getting warmer over the past few decades, or not?". The table below shows the
distribution of responses by party and ideology, where the counts have been replaced
with relative frequencies.
EW NW DK Total
CR 0.06 0.17 0.02 0.25
M/L R 0.12 0.04 0.03 0.19
M/C D 0.13 0.03 0.02 0.18
LD 0.30 0.00 0.08 0.38
Total 0.61 0.24 0.15 1
, a) Are believing that the earth is warming and being a liberal Democrat mutually
exclusive?
b) What is the probability that a randomly chosen respondent believes the earth is
warming or is a liberal Democrat?
c) What is the probability that a randomly chosen respondent believes the earth is
warming given that they are a liberal Democrat?
d) What is the probability that a randomly chosen respondent believes the earth is
warming give - Answer a) not mutually exclusive
b) (.61+.38-.30) = .6900
EW+LD-(LD and EW)
c) (.30/.38) = .7895
(LD and EW)/LD
d) (.06/.25) = .2400
(CR and EW)/CR
e) belief in global warming and party ideology are dependent
f) (.04/.24) = .1667
(MLR and NW)/(NW)
2.20 Assortative mating: Assortative mating is a nonrandom mating pattern where
individuals with similar genotypes and/or phenotypes mate with one another more
frequently than what would be expected under a random mating pattern. Researchers
studying this topic collected data on eye colors of 215 Scandinavian men and their
female partners. The table below summarizes the results (rows represent male eye
color while columns represent female eye color). For simplicity, we only include
heterosexual relationships in this exercise.(please round any numerical answers to 4
decimal places)
Blue Brown Green Total
Blue 47 20 28 95
Brown 18 22 15 55
Green 16 11 38 65
Total 81 53 81 215
a) What is the probability that a randomly chosen male respondent or his partner has
blue eyes?
b) What is the probability that a randomly chosen male respondent with blue eyes has a
partner with blue eyes?
QUESTIONS WITH CORRECT ANSWERS
2.2 Roulette wheel: The game of roulette involves spinning a wheel with 38 slots: 18
red, 18 black, and 2 green. A ball is spun onto the wheel and will eventually land in a
slot, where each slot has an equal chance of capturing the ball.
a) You watch a roulette wheel spin 4 consecutive times and the ball lands on a red slot
each time. What is the probability that the ball will land on a red slot on the next spin?
(please round to four decimal places)
b) You watch a roulette wheel spin 210 consecutive times and the ball lands on a red
slot each time. What is the probability that the ball will land on a red slot on the next
spin? (please round to four decimal places) - Answer a) 18(red)/38(total slots) = .4737
b) 18(red)/38(total slots) = .4737
2.5 Coin Flips: If you flip a fair coin 8 times, what is the probability of each of the
following?(please round all answers to 4 decimal places)
a) getting all tails?
b) getting all heads?
c) getting at least one tails? - Answer a) (1/2)(tails)^8(flips) = 0.0039
b)(1/2)(heads)^8(flips) = 0.0039
c) 1 - (1/2)^8 = 0.9960
2.6 Dice Rolls: If you roll a pair of fair dice, what is the probability of each of the
following? (round all answers to 4 decimal places)
a) getting a sum of 1?
b) getting a sum of 5?
c) getting a sum of 12? - Answer a) 0.0000
minimum = 2
b) 4(combinations)/36(6^2) = 0.1111
,c) 1(combinations)/36(6^2) = 0.0278
2.9 Disjoint vs. independent: In parts (a) and (b), identify whether the events are disjoint,
independent, or neither (events cannot be both disjoint and independent).
a) You and a randomly selected student from your class both earn A's in this course.
b) You and your class partner both earn A's in this course.
c) If two events can occur at the same time, they must be independent. - Answer a)
independent
b) neither
c) false
2.10 Guessing on an exam: In a multiple choice exam, there are 6 questions and 4
choices for each question (a, b, c, d). Nancy has not studied for the exam at all and
decides to randomly guess the answers. What is the probability that:(please round all
answers to four decimal places)
a) the first question she gets right is question number 5?
b) she gets all of the questions right?
c) she gets at least one question right? - Answer a) (3/4)^4*(1/4) = .0791
b) (1/4)^6 = .0002
c) 1-(3/4)^6 = .8220
2.17 Global warming: A research poll asked 1499 Americans "From what you've read
and heard, is there solid evidence that the average temperature on earth has been
getting warmer over the past few decades, or not?". The table below shows the
distribution of responses by party and ideology, where the counts have been replaced
with relative frequencies.
EW NW DK Total
CR 0.06 0.17 0.02 0.25
M/L R 0.12 0.04 0.03 0.19
M/C D 0.13 0.03 0.02 0.18
LD 0.30 0.00 0.08 0.38
Total 0.61 0.24 0.15 1
, a) Are believing that the earth is warming and being a liberal Democrat mutually
exclusive?
b) What is the probability that a randomly chosen respondent believes the earth is
warming or is a liberal Democrat?
c) What is the probability that a randomly chosen respondent believes the earth is
warming given that they are a liberal Democrat?
d) What is the probability that a randomly chosen respondent believes the earth is
warming give - Answer a) not mutually exclusive
b) (.61+.38-.30) = .6900
EW+LD-(LD and EW)
c) (.30/.38) = .7895
(LD and EW)/LD
d) (.06/.25) = .2400
(CR and EW)/CR
e) belief in global warming and party ideology are dependent
f) (.04/.24) = .1667
(MLR and NW)/(NW)
2.20 Assortative mating: Assortative mating is a nonrandom mating pattern where
individuals with similar genotypes and/or phenotypes mate with one another more
frequently than what would be expected under a random mating pattern. Researchers
studying this topic collected data on eye colors of 215 Scandinavian men and their
female partners. The table below summarizes the results (rows represent male eye
color while columns represent female eye color). For simplicity, we only include
heterosexual relationships in this exercise.(please round any numerical answers to 4
decimal places)
Blue Brown Green Total
Blue 47 20 28 95
Brown 18 22 15 55
Green 16 11 38 65
Total 81 53 81 215
a) What is the probability that a randomly chosen male respondent or his partner has
blue eyes?
b) What is the probability that a randomly chosen male respondent with blue eyes has a
partner with blue eyes?
