# 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).

Question
Probability
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).

2020-10-28
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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