Question

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

• A. $\frac{6}{13}$
• B. $\frac{6}{17}$
• C. $0.315$
• D. $0.352$

Answer 1

Answer: (B), (D)

The correct options are
B $\frac{6}{17}$
D $0.352$

Events A and B are independent then $P(A\bigcap B)=0$

$P(A\bigcup B)=P\left(A\right)+P\left(B\right)-P\left(A\right).P\left(B\right)$

Given: $P\left(A\right)=0.15$

$P(A\bigcup B)=0.45$

$\therefore P\left(B\right)=P(A\bigcup B)-P\left(A\right)+P\left(A\right)P\left(B\right)$

$P\left(B\right)=0.45-0.15+1.15P\left(B\right)$

$P\left(B\right)=0.3+0.15P\left(B\right)$

$P\left(B\right)(1-0.15)=0.3$

$P\left(B\right)\left(0.85\right)=0.3$

$P\left(B\right)=\frac{0.3}{0.85}=0.352=\frac{6}{17}$