A die is thrown 6 times and getting a multiple of 3 is a success. Find the probability of getting at most 5 successes.

Solution

Here n = 6, p = P(3, 6) = $2 over 6 space equals 1 third comma space space straight q space equals space 1 minus 1 third space equals 2 over 3$
P(atmost 5 successes) = 1 - P(6) = $1 minus straight C presuperscript 6 subscript 6 space open parentheses 1 third close parentheses to the power of 6 space equals space 1 minus 1 over 729 space equals 728 over 729$