ACTUARY Mathematics and Statistics 1

Question 1

A die is rolled. What is the probability of rolling a number greater than 4?

Accepted Answer

1/3

Answer

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?

Accepted Answer

8

Answer

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,

Accepted Answer

0.94

Answer

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?

Accepted Answer

3/8

Answer

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?

Accepted Answer

1/3

Answer

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

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Actuary Certification Practice Test

Actuary Certification Practice Test

ACTUARY Mathematics and Statistics 1