Question

What is the probability that at least one of a pair of fair dice lands on 6, given the sum of the dice $i$$i,i=2,3,...,12$ ?

Short answer

$\begin{array}{rl}& P(A\mid E_7)=0.33\\ & P(A\mid E_8)=0.40\\ & P(A\mid E_9)=0.50\\ & P(A\mid E_{10})=0.67\\ & P(A\mid E_{11})=1\\ & P(A\mid E_{12})=1\end{array}$

Step-by-step solution

Given Information

Two dice are rolled.

The Sum of numbers on dice is 2 to 12.

Calculation

The sample space when you roll two dice is given below:

As it is required to find the probability that one dice out of two must showed up $6$, means the sum on two dice must be greater than equal to $7$. Therefore, probabilities that at least one of two dice showed up $6$and sum is equal to $(2,3,4,5,6)$is equal to $0$.