Utah General Contractor's Course - Business and Law Exam Prep 100% VERIFIED CORRECT NEW!! 2025/2026

Utah General Contractor's Course - Business and
Law Exam Prep 100% VERIFIED CORRECT NEW!!
2025/2026




MGF1131 Comprehensive Practice Exam: Sections 11.4, 11.6-11.9


Section 11.4: Fundamentals of Probability (Questions 1-35)


Question 1
A bag contains 6 red marbles, 4 blue marbles, and 5 green marbles. If one marble
is drawn at random, what is the probability that it is either blue or green?
A) 4/15
B) 5/15
C) 9/15
D) 3/5
Answer: D) 3/5
*Explanation: Total marbles = 6 + 4 + 5 = 15. Blue or green marbles = 4 + 5 = 9.
Probability = 9/15 = 3/5.*


Question 2
A fair six-sided die is rolled. What is the probability of rolling a number less than 3
or an even number?
A) 1/6
B) 1/3

,C) 2/3
D) 5/6
Answer: D) 5/6
*Explanation: Numbers less than 3: {1,2}. Even numbers: {2,4,6}. Union: {1,2,4,6} =
4 outcomes. Wait, that's 4/6 = 2/3? Let me recalculate carefully. Less than 3: 1,2
(2 outcomes). Even: 2,4,6 (3 outcomes). Overlap (both less than 3 AND even): {2}
(1 outcome). Using inclusion-exclusion: 2/6 + 3/6 - 1/6 = 4/6 = 2/3. But 2/3 is
option C, not D. Did I miss something? Let's list all outcomes: 1,2,3,4,5,6.
Condition: less than 3 OR even. Numbers that satisfy: 1 (less than 3), 2 (both), 4
(even), 6 (even). That's {1,2,4,6} = 4 outcomes. Probability = 4/6 = 2/3. So answer
should be C, not D. I need to correct this.*
*Corrected Answer: C) 2/3*


Question 3
Two fair coins are flipped. What is the probability of getting at least one head?
A) 1/4
B) 1/2
C) 3/4
D) 1
Answer: C) 3/4
*Explanation: Total outcomes: HH, HT, TH, TT = 4. At least one head means not
both tails. Outcomes with at least one head: HH, HT, TH = 3. Probability = 3/4.*


Question 4
A card is drawn from a standard 52-card deck. What is the probability of drawing
a face card (Jack, Queen, King) or a diamond?
A) 12/52
B) 13/52
C) 22/52
D) 25/52

,Answer: D) 25/52
*Explanation: Face cards: 12 (J,Q,K of each suit). Diamonds: 13. Overlap: Face
cards that are diamonds: J , Q , K = 3. Using inclusion-exclusion: 12/52 +
13/52 - 3/52 = 22/52? Wait, 12+13=25, minus 3 = 22. So 22/52 = 11/26. That's not
matching any option. Let me check: 12+13=25, 25-3=22. Yes, 22/52. Option C is
22/52. So answer is C.*
*Corrected Answer: C) 22/52*


Question 5
A bag contains 3 red, 5 white, and 2 blue marbles. Two marbles are drawn
without replacement. What is the probability that both are white?
A) 5/10
B) 20/90
C) 25/100
D) 2/9
Answer: D) 2/9
*Explanation: Total marbles = 10. P(first white) = 5/10 = 1/2. After removing one
white, 9 marbles left, 4 white. P(second white) = 4/9. P(both white) = (1/2) × (4/9)
= 4/18 = 2/9.*


Question 6
From a standard 52-card deck, two cards are drawn without replacement. What is
the probability of drawing two aces?
A) 1/169
B) 1/221
C) 4/52
D) 1/13
Answer: B) 1/221
*Explanation: P(first ace) = 4/52 = 1/13. After drawing an ace, 51 cards left, 3
aces. P(second ace) = 3/51 = 1/17. P(both aces) = (1/13) × (1/17) = 1/221.*

, Question 7
A die is rolled and a coin is flipped. What is the probability of rolling a 5 and
getting tails?
A) 1/6
B) 1/12
C) 1/2
D) 1/3
Answer: B) 1/12
*Explanation: Independent events. P(5) = 1/6. P(tails) = 1/2. P(5 and tails) = (1/6)
× (1/2) = 1/12.*


Question 8
In a class of 30 students, 18 are female, 12 are male. 10 females are wearing
glasses, and 4 males are wearing glasses. If a student is chosen at random, what is
the probability they are female or wearing glasses?
A) 18/30
B) 22/30
C) 26/30
D) 28/30
Answer: C) 26/30
*Explanation: P(F) = 18/30. P(G) = (10+4)/30 = 14/30. P(F and G) = 10/30. P(F or G)
= 18/30 + 14/30 - 10/30 = 22/30? Wait, 18+14=32, minus 10=22. So 22/30 =
11/15. That's option B. Let me verify numbers: Total with glasses = 14. Female or
glasses = all females (18) plus males with glasses (4) = 22. Yes, 22/30. So answer is
B.*
*Corrected Answer: B) 22/30*


Question 9
Events A and B are independent. P(A) = 0.4 and P(B) = 0.5. What is P(A and B)?