Question

Let P(A) = 0.62, P(B) = 0.27, and P(A | B) = 0.42.

a. Calculate P(A ∩ B). (Round your answer to 3 decimal places.)

b. Calculate P(A U B). (Round your answer to 3 decimal places.)

c. Calculate P(B | A). (Round your answer to 3 decimal places.)

Answer 1

a)

Using conditional formula,

P(A | B) = P(A B) / P(B)

0.42 = P(A B) / 0.27

P(A B) = 0.42 * 0.27

= 0.113

b)

P(A B) = P(A) + P(B) - P(A B)

= 0.62 + 0.27 - 0.113

= 0.777

c)

P(B | A) =  P(A B) / P(A)

= 0.113 / 0.62

= 0.182