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Probability

Question

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

Solution

Here n = 5
Let p be the probability of getting an odd number

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

P(at least 4 successes) = P(4) + P(5)

equals space straight C presuperscript 5 subscript 4 space open parentheses 1 half close parentheses space open parentheses 1 half close parentheses to the power of 4 space plus space straight C presuperscript 5 subscript 5 space open parentheses 1 half close parentheses to the power of 5 space equals space open parentheses 1 half close parentheses to the power of 5 space space open square brackets straight C presuperscript 4 subscript 4 space plus space straight C presuperscript 5 subscript 5 close square brackets space equals 1 over 32 open parentheses 5 over 1 plus 1 close parentheses space equals 6 over 32 space equals 3 over 16

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