Question

If events A and B are independent and P(A) = 0.15, (P$\cup$B) = 0.45 then P(B) = ?

• A. $\frac{6}{13}$
• B. $\frac{6}{17}$
• C. $\frac{6}{19}$
• D. $\frac{6}{23}$

Answer 1

The correct option is B $\frac{6}{17}$

$P(A\cap B)=P\left(A\right)\times P\left(B\right)=0.15\times P\left(B\right)$

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

$0.45=0.15+P\left(B\right)-\left(0.15\right)\times P\left(B\right)$

$=0.15+P\left(B\right)(1-0.15)$

$=0.15+0.85P\left(B\right)$

$\therefore 0.85P\left(B\right)=0.45-0.15=0.30$

$\therefore P\left(B\right)=\frac{0.30}{0.85}=\frac{30}{85}=\frac{6}{17}$