# It is Known that 10% of Certain Articles Manufactured Are Defective. What is the Probability that in a Random Sample of 12 Such Articles, 9 Are Defective? - Mathematics and Statistics

Sum

It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective?

#### Solution

The repeated selections of articles in a random sample space are Bernoulli trails. Let X denote the number of times of selecting defective articles in a random sample space of 12 articles.

Clearly, X has a binomial distribution with n = 12 and p = 10% = 10/100 = 1/10

q = 1 - p = 1 - 1/10 = 9/10

Given: n = 12

∴ X ~ B (12, 1/10)

The p.m.f. of X is given by

P[X = x] = "^nC_x  p^x  q^(n - x)

i.e. p(x) = "^12C_x (1/10)^x (9/10)^(12 - x), x = 1, 2, 3,...,12

P(9 defective articles) = P[X = 9]

= p(9) = "^12C_9 (1/10)^9 (9/10)^(12 - 9)

= (12!)/(9!  3!) (1/10)^9 (9/10)^3

= (12 xx 11 xx 10 xx 9!)/(9! xx 3 xx 2 xx 1) xx 1/10^9 xx 9^3/10^3

= 2 xx 11 xx 10 * 9^3/10^12 = 22 (9^3/10^11)

Hence, the probability of getting 9 defective articles =22 (9^3/10^11).

Concept: Bernoulli Trials and Binomial Distribution
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#### APPEARS IN

NCERT Class 12 Maths
Chapter 13 Probability
Q 13 | Page 578