A pair of dice is thrown 7 times. If getting a total of 9 is considered a success, what is the probability of at most 6 successes?

Solution

Here n = 7
In a throw of pair of dice, we get total of 9 when we get (3, 6), (4, 5), (5, 4), (6, 3)
$therefore space space space straight p space equals space 4 over 36 space equals 1 over 9 comma space space space straight q space space equals space 1 space minus space straight p space equals space 1 minus 1 over 9 space equals 8 over 9$
P(atmost 6 successes) = 1 - P(7) = 1 - $straight C presuperscript 7 subscript 7 space open parentheses 1 over 9 close parentheses to the power of 7 space equals space 1 space minus space open parentheses 1 over 9 close parentheses to the power of 7 space equals space 1 minus open parentheses 1 over 9 close parentheses to the power of 7.$

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Probability

A pair of dice is thrown 7 times. If getting a total of 9 is considered a success, what is the probability of at most 6 successes?

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