Question

Given P(A)=$0.5,$P(B)=$0.2$ and P(AB)=0.1;find

• A. $P\left(A\cup B\right)$
• B. $P\left(\overline{A}\cap B\right)$
• C. $P\left(A\cup \overline{B}\right)$
• D. $P\left(\overline{A}\cap \overline{B}\right)$

Answer 1

The correct option is B $P\left(\overline{A}\cap B\right)$

$P\left(A\right)=0.5$

$P\left(B\right)=0.2$

$P\left(AB\right)=0.1$

$\left(a\right)$ $P(A\cup B)=P\left(A\right)+P\left(B\right)-P\left(A\right)P\left(B\right)$

$=[0.5+0.2-(0.5\left)\right(0.2\left)\right]$

$\Rightarrow 0.7-0.1$

$\Rightarrow 0.6$

$\left(b\right)$ $P(\overline{A}\cup B)=\left(P\right(B)-P(A\cap B\left)\right)$

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P\left(\right(A\cap B\left)\right)$

$\Rightarrow 0.3=0.5+0.2-P(A\cap B)$

$P(A\cap B)=0.1$

$\because P(\overline{A}\cap B)=0.2-0.1$

$=0.1$