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Probability

Short Answer Type

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.

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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.

Let p be the probability of throwing 4
$therefore space space space space straight p space equals space 1 over 6 comma space space space straight q space equals space 1 minus straight p space equals space 1 minus 1 over 6 space equals space 5 over 6$
P(at least one die shows up) = 1 - P(0)
$equals space 1 minus straight C presuperscript 4 subscript 0 space open parentheses 1 over 6 close parentheses to the power of 0 space open parentheses 5 over 6 close parentheses to the power of 4 space equals space 1 minus space 1 space cross times space 1 space cross times space 625 over 1296 space equals space 1 minus 625 over 1296 space equals space fraction numerator 1296 minus 625 over denominator 1296 end fraction space equals 671 over 1296.$

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