Out of students in a school, it is known that 65% reside in hostel and 35% are day scholars. Previous year results report that 40% of the students who reside in hostel attain A grade and 20% of day scholars attain A grade in their annual examination. At the end of the year, one student is chosen at random from the class.

Probability of the selected student attaining grade A is:

$\frac{33}{100}$

The correct answer is Option (1) - $\frac{33}{100}$

H → Hostel resident, D → Day scholars

$P(H)=\frac{65}{100}, P(D)=\frac{35}{100}$

A → attained grade A

$P(A|H)=\frac{40}{100}, P(A|D)=\frac{20}{100}$

so $P(A)=P(H)P(A|H)+P(D)P(A|D)$

$=\frac{65}{100}×\frac{40}{100}+\frac{35}{100}×\frac{20}{100}$

$=\frac{33}{100}$