Statistics And Probability Question 499
Question: The probability that a student is not a swimmer is 1/5. What is the probability that out of 5 students, 4 are swimmers
[DCE 1999]
Options:
A) $ {}^{5}C_4{{( \frac{4}{5} )}^{4}}\frac{1}{5} $
B) $ {{( \frac{4}{5} )}^{4}}\frac{1}{5} $
C) $ {}^{5}C_1\frac{1}{5}{{( \frac{4}{5} )}^{4}}\times {}^{5}C_4 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
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The probability that student is not swimmer $ p=\frac{1}{5} $ and probability that student is swimmer $ q=\frac{4}{5} $ .
$ \therefore $ Probability that out of 5 students 4 are swimmer $ ={}^{5}C_4{{( \frac{4}{5} )}^{4}}{{( \frac{1}{5} )}^{5-4}}={}^{5}C_4{{( \frac{4}{5} )}^{4}}( \frac{1}{5} ). $
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