Question

Of the students in a college, it is known that $60\%$ reside in hostel and $40\%$ are day scholars (not residing in hostel). Previous year results report that $30\%$ of all students who reside in hostel attain A grade and $20\%$ of day scholar attain A grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an A grade, what is the probability that the student is a hostile?

• A. $\frac{5}{13}$
• B. $\frac{9}{13}$
• C. $\frac{8}{13}$
• D. None of these

Answer 1

Answer: (B)

$\frac{9}{13}$

Let $A$ denote $A-grade$.

$H$ denote from hostel.

$D$ denote day scholar.

$P\left(A/H\right)=0.3$ and $P\left(A/D\right)=0.2$

$P\left(H\right)=0.6$ and $P\left(D\right)=0.4$

$P\left(H/A\right)=\frac{P\left(A/H\right)\times P\left(H\right)}{P\left(A/H\right)\times P\left(H\right)+P\left(A/D\right)\times P\left(D\right)}$

$P\left(H/A\right)=\frac{0.3\times 0.6}{0.3\times 0.6+0.2\times 0.4}$

$P\left(H/A\right)=\frac{0.18}{0.18+0.08}$

$P\left(H/A\right)=\frac{18}{26}=\frac{9}{13}$