Question

Union and intersection Suppose C and D are two events such that P(C)$=0.6$, P(D)$=0.45$, and

P(C ∪ D)$=0.75$. Find P(C ∩ D).

Short answer

The P$\left(C\cap D\right)$ is$0.30$.

Step-by-step solution

Given Information

We are given the values of P (C)$=0.6$,P (D)$=0.45$,Prole="math" localid="1653986355948" $\left(C\cup D\right)=0.75$ and we have to find out the value of P$\left(C\cap D\right)$.

Explanation

Apply the union rule of probability,

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

P(C)$=0.6$ ,P(D)$=0.45$ ,P$\left(C\cup D\right)=0.75$

Put these valuesinto union rules.

We get$P\left(C\cap D\right)=0.6+0.45-0.75=0.30$

Hence, the value of the probability of intersection between C and D is$0.30$.