Question

The probability that a ${}^{\prime }P$ and $C^{\prime }$ question wil be asked in $IITJEE$ is $\frac{2}{5}$ and probability question is asked is $\frac{4}{7}$. If the probability of getting at least one of them is $\frac{2}{3}$ what is the probability that questions from both the topics are asked.

• A. 17/105
• B. 16/105
• C. 1/35
• D. 6/35

Answer 1

The correct option is A

17/105

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

$\frac{2}{3}=\left(\frac{2}{5}\right)+\left(\frac{4}{7}\right)-x$

$x=\frac{17}{105}$