Question 11 Mark
If A and B are two independent evets, then write $\text{P}(\text{A}\cap\overline{\text{B}})$ in terms of P(A) and P(B).
Answer
View full question & answer→A and B are two independent events
$\therefore\ \text{P}(\text{A}\cap\overline{\text{B}})=\text{P(A)}\text{ P}(\overline{\text{B}})$
$=\text{P(A)}[1-\text{P(B)}]$
$=\text{P(A)}-\text{P(A)}\text{P(B)}$
$\therefore\ \text{P}(\text{A}\cap\overline{\text{B}})=\text{P(A)}\text{ P}(\overline{\text{B}})$
$=\text{P(A)}[1-\text{P(B)}]$
$=\text{P(A)}-\text{P(A)}\text{P(B)}$