Question

Suppose A and B are mutually exclusive events, and that P(B)=0.03 and P(A OR B)=0.52. Find P(A)

Answer 1

Answer:

P(A) = 0.49

Step-by-step explanation:

Given:

A and B are mutually exclusive events.

P(B) = 0.03

P(A or B) = 0.52

If two events A and B are mutually exclusive events, then there are no elements common in both the events. So, the probability of their intersection is 0.

Now, as per probability addition theorem:

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

For mutually exclusive events, P(A and B) = 0. So,

P(A or B) = P(A) + P(B) + 0

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

Plug in the given values and solve for P(A). This gives,

0.52 = P(A) + 0.03

P(A) = 0.52 - 0.03

P(A) = 0.49

Therefore, the probability of occurrence of event A is P(A) = 0.49.