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  • Need solution for RD Sharma Maths Class 12 Chapter 30 Probability Exercise 30.3 question 17.

Need solution for RD Sharma Maths Class 12 Chapter 30 Probability Exercise 30.3 question 17.

Answers (1)

Answer: P(B \mid A)=\frac{n(A \mid B)}{n(A)}=\frac{3}{6}=\frac{1}{2}

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

 

Given,

            A = 4 appears on first die

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

Solution:

 \begin{aligned} &A=\{(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)\} \\ &n(A)=6 \\ &B=\left\{\begin{array}{l} (2,6),(3,5),(3,6),(4,4),(4,5), \\ (4,6),(5,3),(5,4),(5,6),(6,2), \\ (6,3),(6,4),(6,5),(6,6) \end{array}\right\} \\ &n(B)=15 \end{aligned}

Now,

\begin{aligned} &P(A)=6 \\ &P(B)=15 \\ &A \cap B=\{(4,4),(4,5),(4,6)\} \end{aligned}

 Required Probability P(B \mid A)=\frac{P(A \mid B)}{P(A)}=\frac{1}{2}

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