If a and b are events with p(a) = 0.5, p(a or b) = 0.65, p(a and b) = 0.15, find p(b).

P(B) = 0.30

Step-by-step explanation:

This is a probability problem that can be modeled by a diagram of Venn.

We have the following probabilities:

In which is the probability that only A happens.

To find P(B), first we have to find , that is the probability that only B happens.

Finding :

The problem states that P(A OR B) = 0.65. This is the probability that at least one of this events happening. Mathematically, it means that:

The problem states that P(A) = 0.5 and . So we can find .

Replacing it in equation 1)

Since

answer: 1) twenty-seven times y

              2) twenty-seven multiplied by y