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  • Need solution for RD Sharma Maths Class 12 Chapter 30 Probability Exercise 30.3 question 18.

Need solution for RD Sharma Maths Class 12 Chapter 30 Probability Exercise 30.3 question 18.

Answers (1)

Answer: \frac{3}{25}

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

Given,

            A=At least one die does not show 5

            B=The sum of the numbers on two dice is 8

Solution:

Clearly,
            

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

 Required Probability  =P(B \mid A)=\frac{P(A \cap B)}{P(A)}=\frac{3}{25}

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