Question

Events A and B are independent. The P(A) = 3/5, and P(not B) = 2/3. What is P(A and B)?

Answer 1

Given:

Events A and B are independent.

P(A)=

`(3)/(5)`

P(not B)=

`(2)/(3)`

Required:

P(A and B).

Answer:

We have given that P(A)=

`(3)/(5)`

P(not B)=

`(2)/(3)`

Then P(B)=

`\begin{gathered} P(B)=1-P(not\text{ B}) \\ P(B)=1-(2)/(3)=(1)/(3) \end{gathered}`

Hence, P(A and B)=

`P(A)\cdot P(B)=(3)/(5)*(1)/(3)=(1)/(5)`

Final Answer:

P(A and B)=

`(1)/(5)`