Question

Find the probability of 4 turning up at least once in two tosses of a fair die.

Answer 1

Let X be the probability of getting 4 in two tosses of a fair die.
X follows a binomial distribution with n =2; $p\mathit{}=\frac{1}{6}\mathrm{and}q=\frac{5}{6};$
$$\begin{gathered} \mathrm{P}(X=r)={}^{2}C_r{\left(\frac{1}{6}\right)}^r{\left(\frac{5}{6}\right)}^{2-r} \\ \mathrm{Prob}\text{ability}\mathrm{of}\mathrm{getting}4\mathrm{at}\mathrm{least}\mathrm{once}=P(X\ge 1) \\ =1-P(X=0) \\ =1-{}^{2}C_0{\left(\frac{1}{6}\right)}^0{\left(\frac{5}{6}\right)}^{2-0} \\ =1-\frac{25}{36} \\ =\frac{11}{36} \end{gathered}$$