Question

Find the probability of throwing at most 2 sixes in 6 throws of a single die.

Solution

Here n = 6
p = P(6) = $1 over 6 comma$ $straight q space equals space 1 minus straight p space equals space 1 space minus space 1 over 6 space equals 5 over 6$
P(at most 2 sixes) = P(0) + P(1) + P(2)
$equals space straight C presuperscript 6 subscript 0 open parentheses 5 over 6 close parentheses to the power of 6 space plus space straight C presuperscript 6 subscript 1 open parentheses 5 over 6 close parentheses to the power of 5 space open parentheses 1 over 6 close parentheses plus straight C presuperscript 6 subscript 2 space open parentheses 5 over 6 close parentheses to the power of 4 space open parentheses 1 over 6 close parentheses squared equals space 1 space cross times space open parentheses 5 over 6 close parentheses to the power of 6 space plus space 6 over 1 cross times open parentheses 5 over 6 close parentheses to the power of 5 space cross times space 1 over 6 plus fraction numerator 6 cross times 5 over denominator 1 cross times 2 end fraction cross times open parentheses 5 over 6 close parentheses to the power of 4 cross times 1 over 6 squared equals space open parentheses 5 over 6 close parentheses to the power of 4 space open square brackets open parentheses 5 over 6 close parentheses squared plus 6 space cross times 5 over 6 plus 1 over 6 plus 15 cross times 1 over 36 close square brackets space space equals open parentheses 5 over 6 close parentheses to the power of 4 space open square brackets 25 over 36 plus 5 over 6 plus 15 over 36 close square brackets equals space open parentheses 5 over 6 close parentheses to the power of 4 space open square brackets fraction numerator 25 plus 30 plus 15 over denominator 36 end fraction close square brackets space equals space open parentheses 5 over 6 close parentheses to the power of 4 space cross times space 70 over 36 space equals space 35 over 18 open parentheses 5 over 6 close parentheses to the power of 4$

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Probability

Find the probability of throwing at most 2 sixes in 6 throws of a single die.

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