Question

Item9

eBookReferences

Check my workCheck My Work button is now enabled1

Item 9

Item 9

Exercise 4-21 Algo

Let P(A) = 0.46, P(B) = 0.41, and P(A ∩ B) = 0.06.

a. Are A and B independent events?

• Yes because P(A | B) = P(A).

• Yes because P(A ∩ B) ≠ 0.

• No because P(A | B) ≠ P(A).

• No because P(A ∩ B) ≠ 0.

b. Are A and B mutually exclusive events?

• Yes because P(A | B) = P(A).

• Yes because P(A ∩ B) ≠ 0.

• No because P(A | B) ≠ P(A).

• No because P(A ∩ B) ≠ 0.

c. What is the probability that neither A nor B takes place? (Round your answer to 2 decimal places.)

Answer 1

Solution:

Using given information we say that the

a. Are A and B independent events?

• No because P(A ∩ B) ≠ 0.

If  P(A ∩ B) = 0 then we say that they are independent

b. Are A and B mutually exclusive events?

• No because P(A ∩ B) ≠ 0.

If they are mutually exclusive then

p(A U B) = p(A) + p(B) but here this not happen so they are not mutually exclusive

c. What is the probability that neither A nor B takes place?

We know that formula

P( A or B ) = 1 - p(A u B)

But P( A U B ) = p(A) + p(B) - P(A ∩ B)

Therefore P(A U B) = 0.46 + 0.41 - 0.06

P(A U B) = 0.81

Therefore P ( A or B ) = 1 - 0.81

Therefore P ( A or B ) = 0.19

Thank You for providing all and clear information..!!

please like it...