NCERT Class XII Mathematics Chapter - - Solutions
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Question : 70
Total: 101
There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?
Solution:
Let p be the probability of defective item =
=
∴ q = 1 =
=
X has a binomial distribution withn = 10 , p =
, q =
∴ P ( X = r ) = n C r q n − r p r
∴ P (not more than one defective item) = P(X = 0) + P(X = 1)
= 10 C 0 q 10 p 0 + 10 C 1 q 9 p 1
= 1 × (
) 10 × 1 + 10 × (
) 9 × (
)
= (
) 9 ×
X has a binomial distribution with
∴ P (not more than one defective item) = P(X = 0) + P(X = 1)
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