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 getting $7$ in exactly $2$ trials out of $7$.

• A. No success
• B. Exactly six successes
• C. Atleast six successes
• D. none of these.

Answer 1

The correct option is D none of these.

$\begin{array}{c}Whentwodicearethrown\\ S=\left(6\right)\times \left(6\right)=36\\ n\left(S\right)=36\\ Now,\\ Forgetting7\\ E=\left(1,6\right),\left(2,5\right),\left(6,1\right),\left(3,4\right),\left(5,2\right)\\ No.oftrials=7\\ p\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}\\ =\frac{6}{36}=\frac{1}{6}\\ q=1-\frac{1}{6}=\frac{5}{6}\\ obabilitythatin7trials,eventEwilloccurs\\ P\left(x=7\right){=}^7{C}_2\times {\left(\frac{1}{6}\right)}^2\times {\left(\frac{5}{6}\right)}^5\\ Hence,optionDistherequiredanswer.\end{array}$