Question

A pair of dice is thrown seven times.
Getting a total of numbers on the two dice to be seven is considered as a success . Find the probability of at most six successes.

Answer 1

Let $p=$ probability of getting a total of $7=\frac{6}{36}=\frac{1}{6}$

$q=1-p=1-\frac{1}{6}=\frac{5}{6}$

Here $n=7$

$P(X=r){=}^n{C}_r{q}^{n-r}{p}^r$

$P$(atmost $6$ successes)$=P$(not $7$ success)

$=1-P\left(7\right)$

$=1{-}^7{C}_7{\left(\frac{5}{6}\right)}^{7-7}{\left(\frac{1}{6}\right)}^7$

$=1-{\left(\frac{1}{6}\right)}^7$