From the production process which turns 5% defective on an average,a sample size 10 is drawn. Find the probability that the sample contains i).no defective ii). at most one defective iii).atleast one defective
Answers
Given : From the production process which turns 5% defective on an average, a sample of size 10 is drawn.
To Find : the probability that the sample contains
i) no defective;
ii) at most one defective;
iii) atleast one defective.?
Solution:
turns 5% defective
Probability of defective p = 0.05
probability of non defective q = 1 -0.05 = 0.95
sample size n = 10
P(x) = ⁿCₓpˣqⁿ⁻ˣ
i) no defective => x = 0
P(0) = ¹⁰C₀(0.05)⁰(0.95)¹⁰ = (0.95)¹⁰ = 0.5987
at most one defective;
= P(0) + P(1)
= ¹⁰C₀(0.05)⁰(0.95)¹⁰ + ¹⁰C₁(0.05)¹(0.95)⁹
= (0.95)¹⁰ + 0.5(0.95)⁹
= (0.95)⁹ (0.95 + 0.5)
= (0.95)⁹ (1.45)
= 0.91386
atleast one defective
= 1 - P(0)
= 1 - 0.5987
= 0.4013
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