Q68 / 150 · MHT CET 2009 · Mathematics

Given $P(A)=0.5, P(B)=0.4, P(A \cap B)=0.3$, then $P\left(A^{\prime} / B^{\prime}\right)$ is equal to

  • A
    $1 / 3$
  • B
    $1 / 2$
  • Correct answer
    C
    $2 / 3$
  • D
    $3 / 4$

Solution

$$ \text { } \begin{aligned} P\left(A^{\prime} \mid B^{\prime}\right)=& \frac{P\left(A^{\prime} \cap B^{\prime}\right)}{P\left(B^{\prime}\right)} \\ &=\frac{P(A \cup B)^{\prime}}{P\left(B^{\prime}\right)} \\ &=\frac{1-P(A \cup B)}{1-P(B)} \\ &=\frac{1-[P(A)+P(B)-P(A \cap B)]}{1-P(B)} \\ &=\frac{1-[0.5+0.4-0.3]}{1-0.4} \\ &=\frac{0.4}{0.6} \\ &=\frac{2}{3} \end{aligned} $$

Hence, the correct answer is option: 'C'.

Relevant Questions