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Probability

Short Answer Type

1031. A coin is tossed 6 times. What is the probability of getting at least two heads?

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1032. A coin is tossed 6 times. What is the probability of getting at least four heads?

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1033. A coin is tossed 5 times. What is the probabilities of obtaining at least 2 tails?

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1034. A fair coin is tossed 7 times. Find the probability of obtaining at least 5 tails.

Here n = 7
Let p be the probability of getting a tail

$therefore space space space space space straight p space equals space 1 half comma space space space straight q space equals space 1 minus 1 half space equals space 1 half$

P(at least 5 tails) = P(5) + P(6) + P(7)

$equals space straight C presuperscript 7 subscript 5 space open parentheses 1 half close parentheses squared space open parentheses 1 half close parentheses to the power of 5 plus space space straight C presuperscript 7 subscript 6 space open parentheses 1 half close parentheses space open parentheses 1 half close parentheses to the power of 6 space plus space straight C presuperscript 7 subscript 7 space open parentheses 1 half close parentheses to the power of 7 space equals space open parentheses 1 half close parentheses to the power of 7 space open square brackets straight C presuperscript 7 subscript 5 space plus space straight C presuperscript 7 subscript 6 space plus space straight C presuperscript 7 subscript 7 close square brackets space equals space 1 over 128 open square brackets fraction numerator 7 space cross times 6 over denominator 1 cross times 2 end fraction plus 7 over 1 plus 1 close square brackets space equals space 1 over 128 left parenthesis 21 plus 7 plus 1 right parenthesis space equals space 29 over 128$

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1035. A coin is tossed 3 times. Find the probability of at least two heads.

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1036. A die is thrown 5 times. If getting an odd number is success, find the probability of getting at least 4 successes.

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1037. A die is thrown 6 times. If getting an odd number is a success, what is the probability of at least 5 successes?

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1038. A die is thrown 6 times. Getting a number greater than 4 is considered a success. Find the probability of at least two successes.

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1039. An unbiased die is thrown 3 times. If getting a 2 or 5 is considered a success, find the probability of at least 2 successes.

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1040. Five dice are thrown simultaneously. If the occurrence of 3, 4 or 5 in a single die is considered a success, find the probability of at least three successes.

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