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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?

We get a doublet when we get
(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)
Let p be probability of getting a doublet
$therefore space straight p space equals space 6 over 36 space equals space 1 over 6 space space space space space space straight q space equals space 1 minus straight p space equals space 1 space minus 1 over 6 space equals space 5 over 6$
P(at least two doublets) = 1 - [P(0) + P(1)]
$equals space 1 minus open square brackets straight C presuperscript 4 subscript 0 open parentheses 1 over 6 close parentheses to the power of 0 space open parentheses 5 over 6 close parentheses to the power of 4 space plus space straight C presuperscript 4 subscript 1 space open parentheses 1 over 6 close parentheses to the power of 1 space open parentheses 5 over 6 close parentheses cubed close square brackets space space space space space space space space open square brackets because space space straight P left parenthesis straight r right parenthesis space equals space straight C presuperscript straight n subscript straight r space straight p to the power of straight r space straight q to the power of straight n minus straight r end exponent comma space straight n space equals space 4 close square brackets equals space 1 minus open square brackets 1 cross times 1 cross times 625 over 1296 plus 4 over 1 cross times 1 over 6 cross times 125 over 216 close square brackets space equals space 1 minus open square brackets 625 over 1296 plus 500 over 1296 close square brackets space equals space 1125 over 1296 equals space space fraction numerator 1296 minus 1125 over denominator 1296 end fraction space equals space 171 over 1296$

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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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