Browse Questions

# If A and B are two events such that P (A) = $\large \frac{1}{4}$ , P (B) = $\large\frac{1}{2}$ and P(A $\cap$B) = $\large \frac{1}{8}$ , find P (not A and not B).

$\begin{array}{1 1}3/8 \\ 1/8 \\ 1/4 \\ 5/8 \end{array}$

Toolbox:
• P (not A and not B) = $P(\bar{A}\cap\;\bar{B})$ = $P(\overline{A \cup B})$ = 1 - P (A $\cup$ B)
• P (A $\cup$ B) = P(A) + P(B) - P(A $\cap$ B)
• P ($\bar{A})$ = 1 - P(A)
Given $\;P(A)=\large \frac{1}{4}$, $P(B)=\large \frac{1}{2}$ and $\;P(A\cap\;B)=\large \frac{1}{8}$
P (A $\cup$ B) = P(A) + P(B) - P(A $\cap$ B)
$\Rightarrow \;P(A\cup\;B)=\large \frac{1}{4}+\frac{1}{2}-\frac{1}{8}$ =$\large\;\frac{5}{8}$
$\Rightarrow P(\bar{A}\cap\;\bar{B})=1-P(A\cup\;B)$ =$\;1-\large\frac{5}{8}=\frac{3}{8}$