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:
Answer & explanation
Correct answer: option 1
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 $P(A)=P(H)P(A|H)+P(D)P(A|D)$
$=\frac{65}{100}×\frac{40}{100}+\frac{35}{100}×\frac{20}{100}$
$=\frac{33}{100}$