A pair of dice is thrown 10 times. If getting a doublet is considered a success, find the probability of getting 4 successes.

Solution

Here n = 10
Let p be the probability that doublet is obtained
$therefore space space space straight p space equals space straight P left curly bracket left parenthesis 1 comma space 1 right parenthesis comma space left parenthesis 2 comma space 2 right parenthesis comma space left parenthesis 3 comma space 3 right parenthesis comma space left parenthesis 4 comma space 4 right parenthesis comma space left parenthesis 5 comma space 5 right parenthesis comma space left parenthesis 6 comma space 6 right parenthesis right curly bracket space space space space space space space space space space equals 6 over 36 space equals space 1 over 6 straight q space equals space 1 minus space straight p space equals space 1 minus 1 over 6 space equals space 5 over 6$
Required probability = P(4) = $straight C presuperscript 10 subscript 4 space open parentheses 5 over 6 close parentheses to the power of 6 space open parentheses 1 over 6 close parentheses to the power of 4$
$equals space fraction numerator 10 space cross times space 9 space cross times space 8 space cross times space 7 over denominator 1 space cross times 2 space cross times 3 space cross times 4 end fraction cross times 5 to the power of 6 over 6 to the power of 6 cross times 1 over 6 to the power of 4 space equals 3281250 over 6 to the power of 10$

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Probability

A pair of dice is thrown 10 times. If getting a doublet is considered a success, find the probability of getting 4 successes.

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