# Solve the following problem : In a large school, 80% of the students like mathematics. A visitor asks each of 4 students, selected at random, whether they like mathematics. Find the probability that - Mathematics and Statistics

Sum

Solve the following problem :

In a large school, 80% of the students like mathematics. A visitor asks each of 4 students, selected at random, whether they like mathematics.

Find the probability that the visitor obtains the answer yes from at least 3 students.

#### Solution

Let X denote the number of pupils who like mathematics.

P(pupils like mathematics) = p = (8)/(100) = (4)/(5)   ...[Given]

q = 1 – p = 1 - (4)/(5) = (1)/(5)

Given, n = 4

∴ X ~ B(4, 4/5)
The p.m.f. of X is given by

P(X = x) = ""^4"C"x 4/5^x  (1/5)^(4 - x), x = 0, 1, ...,4

P(the visitor obtains the answer yes from at least 3 students)
= P(X ≥ 3)
= P(X = 3 or X = 4)
= P(X = 3) + P(X = 4)

= ""^4"C"_3 (4/5)^3 (1/5)^1 + (256)/(5^4)     ...[From (i)]

= (4^4)/(5^4) + (256)/(5^4)

= (256)/(5^4) + (256)/(5^4)

= (512)/(5^4).

Concept: Random Variables and Its Probability Distributions
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Probability Distributions
Part II | Q 1.11 | Page 157