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) → \(\displaystyle\frac{33}{100}\)
Let \(E_1\) = the student is a hosteller, \(E_2\) = the student is a day scholar, and A = the student attains grade A.
\(P(E_1) = 0.65,\quad P(E_2) = 0.35\)
\(P(A|E_1) = 0.40,\quad P(A|E_2) = 0.20\)
By the theorem of total probability:
\(P(A) = P(E_1)P(A|E_1) + P(E_2)P(A|E_2)\)
\(= 0.65\times0.40 + 0.35\times0.20\)
\(= 0.26 + 0.07 = 0.33\)
\( \displaystyle P(A) = \frac{33}{100} \)