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In a box containing 100 eggs 10 eggs are...

In a box containing 100 eggs 10 eggs are roten the probability that out of a sample of 5 eggs, none is rotten (if the sampling is with replacement)

A

`((1)/(10))^(5)`

B

`((1)/(5))^(5)`

C

`((9)/(5))^(5)`

D

`((9)/(10))^(5)`

Text Solution

Verified by Experts

The correct Answer is:
D
(d) Here, probability of fresh egg, `p=(90)/(100)=(9)/(10)`
probability of rotten egg, `q=(10)/(100)=(1)/(10)` and n=5
`:.` Required probability `=P(X=5)=""^(5)C_(5)((9)/(10))^(5)((1)/(10))^(0)`
`=1xx((9)/(10))^(5)xx(1)=((9)/(10))^(5)`
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