Question

Consider the following probabilities: P(AC) 0.57, PB = 0.36, and P(A n B) 0.03 a. Find P(A | BC). (Do not round intermediate calculations. Round your answer to 2 decimal places.) P(A | BC) b. Find P(BC | A). (Do not round intermediate calculations. Round your answer to 3 decimal places.) P(BC A) c. Are A and B independent events? Yes because PAI B = PA) Yes because PAN B)0 No because P(A I B)PA). No because PAN B)0

Answer 1

Solution:

Given that,

P(A^c) = 0.57

P(B) = 0.36

P(A $\cap$ B^c) = 0.03

P(A) = 1 - P(A^c)

= 1 - 0.57

= 0.43

P(B^c) = 1 - P(B)

= 1 - 0.36

= 0.64

a)

By using conditional probability

P(A / B^c) = P(A $\cap$ B^c) / P(B^c)

= 0.03 / 0.64

= 0.05

b)

P(B^c / A) = P(A $\cap$ B^c) / P(A)

= 0.03 / 0.43

= 0.070

c)

If A and B are independent

Then

P(A / B^c) = P(A)

The option is

Yes because P(A / B^c) = P(A)