Question

Suppose P(A)=05.0, P(B)=0.75, and A and B are independent. The probability of the complement of the event (A and B) is :

a. 1-(.50 + .25 = .25

b. 0.50 + .25 = .75

c. 1-(.5 x .75) = .625

which is the correct answer?

Answer 1

Solution:

Given:

P(A) =0.50

P(B)= 0.75

A and B are independent.

We have to find:

P(A and B)^c =...........?

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

P(A and B)^c = 1 - [ P(A) x P(B) ]  

(Since A and B are independent , P(A and B) =P(A) x P(B) )

P(A and B)^c = 1 - [ 0.50 x 0.75 ]

P(A and B)^c = 1 - 0.375

P(A and B)^c = 0.625

Thus correct answer is: c. 1-(.5 x .75) = .625