Let A and B be events with P(A)=0.6, P(B)=0.4, and P(B|A)= 0.4. Find P(A and B).

Let A and B be events with P(A)=0.6, P(B)=0.4, and P(B|A)= 0.4. Find P(A and B).

asked 2020-10-27
Let A and B be events with P(A)=0.6, P(B)=0.4, and \(\displaystyle{P}{\left({B}{\mid}{A}\right)}={0.4}\). Find P(A and B).

Answers (1)

From the definition of the conditional probability, \(\displaystyle{P}{\left({B}{\mid}{A}\right)}=\frac{{{P}{\left({A}\ {\quad\text{and}\quad}\ {B}\right)}}}{{P}}{\left({A}\right)}\)
So, \(\displaystyle{P}{\left({A}\ {\quad\text{and}\quad}\ {B}\right)}={P}{\left({A}\right)}{P}{\left({B}{\mid}{A}\right)}={0.6}\cdot{0.4}={0.24}\)

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