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Probability

Question

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

Solution

Here n = 6
Let p be the probability of getting an odd number

space space therefore space space space straight p space equals space straight p left parenthesis 1 comma space 3 comma space 5 right parenthesis space equals space 3 over 6 equals space 1 half comma space space straight q space equals space 1 minus straight p space equals space 1 minus 1 half space equals 1 half

P(at least 5 successes) = P(5) + P(6)

equals space straight C presuperscript 6 subscript 5 space open parentheses 1 half close parentheses to the power of 1 space open parentheses 1 half close parentheses to the power of 5 plus space straight C presuperscript 6 subscript 6 space open parentheses 1 half close parentheses to the power of 6 space equals space open parentheses 1 half close parentheses to the power of 6 space open square brackets straight C presuperscript 6 subscript 5 plus straight C presuperscript 6 subscript 6 close square brackets equals space 1 over 64 left parenthesis 6 plus 1 right parenthesis space equals space 7 over 64

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