Statistics And Probability Question 310
Question: In a box containing 100 eggs, 10 eggs are rotten. The probability that out of a sample of 5 eggs none is rotten if the sampling is with replacement is
[MP PET 1991; MNR 1986; RPET 1995; UPSEAT 2000]
Options:
A) $ {{( \frac{1}{10} )}^{5}} $
B) $ {{( \frac{1}{5} )}^{5}} $
C) $ {{( \frac{9}{5} )}^{5}} $
D) $ {{( \frac{9}{10} )}^{5}} $
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Answer:
Correct Answer: D
Solution:
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Let $ P(fresh\,egg)=\frac{90}{100}=\frac{9}{10}=p $ $ P(rotten\,egg)=\frac{10}{100}=\frac{1}{10}=q $ ; $ n=5, $ $ r=5 $ So the probability that none egg is rotten $ ={}^{5}C_5{{( \frac{9}{10} )}^{5}}.{{( \frac{1}{10} )}^{0}}={{( \frac{9}{10} )}^{5}} $ .
BETA
