# In a large school, 80% of the pupil like Mathemat-ics. A visitor to the school asks each of 4 pupils, chosen at random, whether they like Mathematics. - Mathematics and Statistics

Sum

In a large school, 80% of the pupil like Mathematics. A visitor to the school asks each of 4 pupils, chosen at random, whether they like Mathematics.
Calculate the probabilities of obtaining an answer yes from 0, 1, 2, 3, 4 of the pupils.

#### Solution

Let X = number of pupils like Mathematics.

p = probability that pupils like Mathematics

∴ p = 80% = 80/100 = 4/5

and 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) = "^nC_x  p^x  q^(n - x)

i.e. p(x) = "^4C_x  (4/5)^x  (1/5)^(4 - x) x = 0, 1, 2, 3, 4

The probabilities of obtaining an answer yes from 0, 1, 2, 3, 4 of pupils are P(X= 0), P(X = 1), P(X = 2), P(X = 3) and P(X = 4) respectively.

i.e. "^4C_0  (4/5)^0  (1/5)^(4 - 0), "^4C_1  (4/5)^1  (1/5)^(4 - 1) , "^4C_2  (4/5)^2  (1/5)^(4 - 2), "^4C_3  (4/5)^3  (1/5)^(4 - 3) and "^4C_4  (4/5)^4  (1/5)^(4 - 4)

i.e. 1 (1)(1/5)^4, 4(4/5)*(1/5)^3, (4 xx 3)/(1 xx 2) (16/25)(1/25), 4(64/125)(1/5) and  1 xx (4/5)^4 (1/5)^0

i.e. (1/5)^4, 16/5 (1/5)^3, 96/5^2 (1/5^2), 256/5^3 (1/5) and  256/5^4

i.e. 1/5^4, 16/5^4, 96/5^4, 256/5^4, 256/5^4

OR 1/625, 16/625, 96/625, 256/625 and 256/625

Concept: Binomial Distribution
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 8 Binomial Distribution
Miscellaneous exercise 8 | Q 14.1 | Page 255