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Probability

Question
CBSEENMA12033866
Wired Faculty App

The probability that a bulb produced by a factory will fuse after 150 days of use is 0·05. Find the probability that out of 5 such bulbs more than one will fuse after 150 days of use.

Solution

Here n = 5
               straight p space equals 0.05 space equals space 5 over 100 space equals 1 over 20 comma space space straight q space equals space 1 space minus space straight p space equals space 1 minus 1 over 20 space equals space 19 over 20
P(not more than one bulb will fuse after 150 days)
                            equals space straight P left parenthesis 0 right parenthesis space plus space straight P left parenthesis 1 right parenthesis equals space straight C presuperscript 5 subscript 0 open parentheses 19 over 20 close parentheses to the power of 5 minus 0 end exponent space open parentheses 1 over 20 close parentheses to the power of 0 space plus space straight C presuperscript 5 subscript 1 space open parentheses 19 over 20 close parentheses to the power of 5 minus 1 end exponent space open parentheses 1 over 20 close parentheses to the power of 1 space equals space 1 space cross times space open parentheses 19 over 20 close parentheses to the power of 15 space cross times space 1 space plus space 5 over 1 space cross times space open parentheses 19 over 20 close parentheses to the power of 4 space cross times space 1 over 20 space equals open parentheses 19 over 20 close parentheses to the power of 4 space open square brackets 19 over 20 plus 5 over 20 close square brackets space equals space open parentheses 19 over 20 close parentheses to the power of 4 space cross times space 24 over 20 space equals space 6 over 5 open parentheses 19 over 20 close parentheses to the power of 4

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