UTMA Probability 2 — Questions and Answers
Question 1: A card is drawn from a standard 52-card deck. What is the probability of drawing a king?
- 1/52
- 1/13 (Correct answer)
- 4/52 simplified to 1/13
- 2/13
Correct answer: 1/13
There are 4 kings in 52 cards: P = 4/52 = 1/13.
Question 2: If P(A) = 0.5, P(B) = 0.4, and P(A and B) = 0.2, what is P(A or B)?
- 0.7 (Correct answer)
- 0.9
- 0.2
- 1.1
Correct answer: 0.7
P(A∪B) = P(A) + P(B) − P(A∩B) = 0.5 + 0.4 − 0.2 = 0.7.
Question 3: In how many ways can 3 items be chosen from 7 (order does not matter)?
- 21
- 35 (Correct answer)
- 42
- 210
Correct answer: 35
C(7,3) = 7!/(3!×4!) = (7×6×5)/(3×2×1) = 35.
Question 4: Two events A and B are independent. If P(A) = 0.3 and P(B) = 0.5, what is P(A and B)?
- 0.8
- 0.15 (Correct answer)
- 0.2
- 0.35
Correct answer: 0.15
For independent events: P(A∩B) = P(A) × P(B) = 0.3 × 0.5 = 0.15.
Question 5: A box has 3 defective and 7 non-defective bulbs. What is the probability of drawing 2 non-defective bulbs in a row (without replacement)?
- 49/100
- 42/90
- 7/15 (Correct answer)
- 6/10
Correct answer: 7/15
P = (7/10) × (6/9) = 42/90 = 7/15.
Question 6: What is the expected value if you win $10 with probability 0.3 and lose $5 with probability 0.7?
- $3.00
- −$0.50 (Correct answer)
- −$1.50
- $1.50
Correct answer: −$0.50
E = 10(0.3) + (−5)(0.7) = 3 − 3.5 = −0.50.
UTMA Probability 2
A card is drawn from a standard 52-card deck.
What is the probability of drawing a king?