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1021. 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.

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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1022. 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 at least one will fuse after 150 days of use.

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1023. 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 none will fuse after 150 days of use.

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1024. The probabilities that a bulb produced by a factory will fuse after 160 days is 0·06. Find the probability that out of 5 such bulbs, at the most one bulb will fuse after 160 days of use.

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1025. In four throws with a pair of dice, what is the probability of throwing doublets at least twice?

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1026. A pair of dice is thrown 6 times. If getting a total of 9 is considered a success, what is the probability of at least 5 successes?

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1027. Find the probability of getting a sum of 9 at least twice in 10 throws with two dice.

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1028. A pair of dice is thrown 6 times. If getting a total of 7 is considered a success, what is the probability of at least 4 successes?

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1029. A pair of dice is thrown 6 times. If getting a total of 7 is considered a success, find the probability of at least five successes.

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1030. In a throw of 4 dice, find the probability that at least one die shows up 4.

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1021. 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.