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Need solution for RD Sharma Maths Class 12 Chapter 30 Probability Exercise 30.3 question 20.

Answers (1)

Answer: \frac{2}{5}

Hint: P(A \mid B)=\frac{n(A \cap B)}{n(B)}

Given :- Now, Let A = 5 appears on the die at least once.

               B = The sum of the no. on two dice is 8

Solution:

Clearly,

\begin{aligned} &A=\left\{\begin{array}{l} (1,5),(2,5),(3,5),(4,5),(5,5), \\ (6,5),(5,1),(5,2),(5,3),(5,4), \\ (5,6) \end{array}\right\} \\ &B=\{(2,6),(3,5),(4,4),(5,3),(6,2)\} \\ &A \cap B=\{(3,5),(5,3)\} \end{aligned}       

            
P(A) = 11
P(B) = 5

Required Probability P(A \mid B)=\frac{P(A \cap B)}{P(B)}=\frac{2}{3}

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