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Question
CBSEENMA12033907

In a box containing 100 bulbs, 10 are defective. What is the probabilities that out of a sample of 5 bulbs
(i) none is defective    (ii) exactly two are defective.

Solution

Here n = 5
Let p be the probability of getting defective bulbs
therefore space space space straight p space equals space 10 over 100 space equals space 1 over 10 comma space space space straight q space equals space 1 minus space straight p space equals space 1 minus 1 over 10 space equals space 9 over 10
(i) Required probability  = P(0)
equals space straight C presuperscript 5 subscript 0 space open parentheses 9 over 10 close parentheses to the power of 5 minus 0 end exponent space open parentheses 1 over 10 close parentheses to the power of 0 space equals space 1 space cross times space open parentheses 9 over 10 close parentheses to the power of 5 space equals space open parentheses 9 over 10 close parentheses to the power of 5
(ii) Required probability = P (2)
equals space straight C presuperscript 5 subscript 2 space open parentheses 9 over 10 close parentheses to the power of 5 minus 2 end exponent space open parentheses 1 over 10 close parentheses squared space equals fraction numerator 5 space cross times space 4 over denominator 1 space cross times 2 end fraction cross times 9 over 10 cross times 9 over 10 cross times 9 over 10 cross times 1 over 100 space equals 729 over 10000 space equals.0729

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