ACTUARY Mathematics and Statistics 1 — Questions and Answers
Question 1: A die is rolled. What is the probability of rolling a number greater than 4?
- 1/6
- 1/3 (Correct answer)
- 1/2
- 2/3
Correct answer: 1/3
A standard die has six faces (1 through 6). The numbers greater than 4 are 5 and 6, which are 2 outcomes.
Question 2: A bag contains 3 red balls and 2 blue balls. A ball is randomly drawn. If a red ball is worth 5 points and a blue ball is worth 10 points, what is the expected value of the points earned?
- 6
- 7
- 8 (Correct answer)
- 9
Correct answer: 8
The probability of drawing a red ball is 3/5 , and the probability of drawing a blue ball is 2/5. The expected value is: E(X)=(5⋅3/5 )+(10⋅ 2/5)=3+4=8
Question 3: If a random variable X has the following probability distribution: P(X=1) =0.2, P(X=2) =0.5, P(X=3)=0.3,
- 0.61
- 0.75
- 0.94 (Correct answer)
- 1.02
Correct answer: 0.94
Var(X)=4.9−(2.1) 2 =4.9−4.41=0.94
Question 4: A coin is flipped 3 times. What is the probability of getting exactly 2 heads?
- 1/8
- 3/8 (Correct answer)
- 3/4
- 1/2
Correct answer: 3/8
P(X=2)=3⋅(0.5) 2 ⋅(0.5) 1 =3⋅0.25⋅0.5=3/8
Question 5: A card is drawn from a standard 52-card deck. What is the probability that it is a queen given that it is a face card?
- 1/12
- 1/9
- 1/3 (Correct answer)
- 1/4
Correct answer: 1/3
There are 12 face cards in a deck (3 face cards in each of the 4 suits: J, Q, K). Out of these, 4 are queens. The conditional probability is: P(queen | face card)= total outcomes (face cards)/ favorable outcomes (queens)= 4/12= 1/3
ACTUARY Mathematics and Statistics 1
A die is rolled.
What is the probability of rolling a number greater than 4?