In a random experiment, let A and B be events such that P(A or B) = 0.7, P(A and B) = 0.3 and = 0.4. Find P(B).

Question

Philoid · Accepted Answer

Given : P() = 0.4, P(A or B) = 0.7 and P(A and B) = 0.3

To find : P(B)

Formula used : P(A) = 1 – P()

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

We have P() = 0.4

P(A) = 1 – 0.4 = 0.6

We get P(A) = 0.6

Substituting in the above formula we get,

0.7 = 0.6 + P(B) – 0.3

0.7 = 0.3 + P(B)

0.7 – 0.3 = P(B)

0.4 = P(B)

P(B) = 0.4