Q 3.4 - A First Course in Probability

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$ ?

Step-by-Step Solution

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 1 : Given Information

Two dice are rolled.

The Sum of numbers on dice is 2 to 12.

Step 2: 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 $0$ .