Probability-4 (FRM)

There are 10 students in a class. The probability of a student getting absent is 5%. The probability of any one student getting absent is completely independent of the presence or absence of any other student. What is the probability that exactly one student gets absent?

(a)5%          (b) 50%        (c) 32%              (d) 3%

Solution follows here:

Solution:

It is given that the probability of any one student getting absent is completely independent of the presence or absence of any other student. Hence we need to consider the individual statuses of all the students and get multiply all the probabilities as they are independent events.

P(E) = P(E₁)* P(E₂)* P(E₃)*..... P(E₁₀)

Probability of a student getting absent is = 5% = 0.05

=> Probability of a student getting present = (1-0.05) = 0.95

Exactly one student absent => 9 students present

=> Probability = (0.05)¹(0.95)⁹ = (0.05)(0.63) = 0.0315 = 3.15%

Nearest answer is 3%

Answer (d)