Question

Given that P(A or B) = 13, P(A)= 14, and P(A and B) = 18…. find P(B)Use the addition rule

Answer 1

Answer:

P(B)=17

Explanation:

Given:

• P(A or B) = 13

,

• P(A)= 14

,

• P(A and B) = 18

We want to find the value of P(B).

By the addition rule of probability, if A and B are two events in a probability experiment, then the probability that either one of the events will occur is:

$P(A\text{ or B\rparen}=P(A)+P(B)-P(A\text{ and }B)$

Substitute the given values:

$13=14+P(B)-18$

Then solve for P(B):

$\begin{gathered} P(B)=13+18-14 \\ P(B)=17 \end{gathered}$

The value of P(B) is 17.