Question

If events $A,B$ are independent,$P(A\text{'})=2/3andP(B\text{'})=2/7$ then $P(A\cap B)$ is equal to

• A. $4/21$
• B. $5/21$
• C. $1/21$
• D. $3/21$

Answer 1

The correct option is B

$5/21$

Finding the value of :

Given that $P(A\text{'})=2/3$ and $P(B\text{'})=2/7$

Since $A,B$ are independent events, then

$\begin{array}{rcl}P(A\cap B)& =& \left[\right(1-P(A’)].[(1-P(A’\left)\right]\\ & =& [1-(⅔\left)\right].[1-(2/7\left)\right]\\ & =& (⅓).(5/7)\\ & =& 5/21\end{array}$$\mathbf{}\mathit{P}\mathbf{(}\mathit{A}\mathbf{}\mathbf{\cap }\mathbf{}\mathit{B}\mathbf{)}\mathbf{}\mathbf{=}\mathbf{}\mathit{P}\mathbf{\left(}\mathit{A}\mathbf{\right)}\mathbf{.}\mathbf{}\mathit{P}\mathbf{\left(}\mathit{B}\right)$

Hence, the correct answer is option B