Question

Ashu studies at Byju's classes and her probability of selection in $IIT-JEE$ is $\frac{4}{5}$. Ridhima took coaching at $FIIT-JEE$ and the probability of her selection is $\frac{2}{3}$. What is the probability that only 1 of them cracks the Exam?

• A. 2/5
• B. 3/10
• C. 4/15
• D. None of the above.

Answer 1

The correct option is D

None of the above.

$P\left(A\right)=\frac{4}{5}$

$P\left(R\right)=\frac{1}{3}$

$P\left(E\right)=P\left(A^{\prime }B\right)+P\left(A{B}^{\prime }\right)$

$P\left(E\right)=\frac{1}{5}\times \frac{1}{3}+\frac{4}{5}\times \frac{2}{3}$

$P\left(E\right)=\frac{1}{15}+\frac{8}{15}$

$P\left(E\right)=\frac{9}{15}$

$P\left(E\right)=\frac{3}{5}$