Question

Union and intersection Suppose A and B are two events such that P (A)$=0.3$, P (B)$=0.4$, and

P (A∪B)$=0.58$. Find P (A∩B).

Short answer

The P$(A\cap B)$is$0.12$.

Step-by-step solution

Given Information

We are given the values of P (A)$=0.3$,P (B)$=0.4$, P$\left(A\cup B\right)=0.58$and we have to find out the value of P$\left(A\cap B\right)$.

Explanation

Apply the union rule of probability,

which states that$P(A\cup B)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)$

P(A)$=0.3$,P(B)$=0.4$,P$(A\cup B)=0.58$.

Put these valuesinto union rules.

We get$P\left(A\cap B\right)=0.4+0.3-0.58=0.12$

Hence, the value of the probability of intersection between A and B is$0.12$.