Answer to Question #216697 in Statistics and Probability for Prash

Question

A pair of dice is thrown twice .Find the Probability of scoring 7 points

i) once ii) twice and iii) atleast once

Using binomial distribution

Answer 1

The probability a roll of two dice will add to 7 is $\frac{6}{36}=\frac{1}{6}.$

So, we have a binomial distribution with $n=2,\;p=\frac{1}{6}.$

i) $P(X=1)=C_2^1(\frac{1}{6})^1(\frac{5}{6})^1=\frac{5}{18}.$

ii) $P(X=2)=C_2^2(\frac{1}{6})^2=\frac{1}{36}.$

iii) $P(X\ge1)=1-P(X=0)=1-C_2^0(\frac{5}{6})^2=\frac{11}{36}.$