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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.

Here n = 10
We get total of 9 when we get, (3, 6), (4, 5), (5, 4), (6, 3)
$therefore space space space space straight p space equals space 4 over 36 space equals space 1 over 9 comma space space straight q space equals space 1 minus space straight p space equals space 1 space minus space 1 over 9 space equals space 8 over 9$
P(getting sum 9 at least twice) = 1 - [P(0) + P(1)]
$equals space 1 minus space open square brackets straight C presuperscript 10 subscript 0 space open parentheses 1 over 9 close parentheses to the power of 0 space open parentheses 8 over 9 close parentheses to the power of 10 space plus space straight C presuperscript 10 subscript 1 space open parentheses 1 over 9 close parentheses to the power of 1 space open parentheses 8 over 9 close parentheses to the power of 9 close square brackets space equals space 1 minus open square brackets 1 space cross times space 1 space cross times space open parentheses 8 over 9 close parentheses to the power of 10 plus space 10 over 1 cross times 1 over 9 cross times open parentheses 8 over 9 close parentheses to the power of 9 close square brackets space equals 1 minus open parentheses 8 over 9 close parentheses to the power of 9 space open square brackets 8 over 9 plus 10 over 9 close square brackets space equals space 1 minus open parentheses 8 over 9 close parentheses squared space left parenthesis 2 right parenthesis space equals space 1 minus space 2 space open parentheses 8 over 9 close parentheses to the power of 9$