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  • Provide solution for RD Sharma Maths Class 12 Chapter 30 Probability Exercise 30.3 question 27.

Provide solution for RD Sharma Maths Class 12 Chapter 30 Probability Exercise 30.3 question 27.

Answers (1)

Answer: \frac{1}{2},\frac{1}{3}

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

Given,  A=Both the children are girls

            B=The youngest child is a girl   
            C=At least one child is a girl

Solution:

\begin{aligned} &S=\left\{B_{1} B_{2}, B_{1} G_{2}, G_{1} B_{2}, G_{1} G_{2}\right\} \\ &A=\left\{G_{1} G_{2}, G_{2} G_{1}\right\} \\ &B=\left\{B_{1} G_{2}, G_{1} G_{2}\right\} \\ &C=\left\{B_{1} G_{2}, G_{1} B_{2}, G_{1} G_{2}\right\} \\ &A \cap B=\left\{G_{1} G_{2}\right\} \\ &A \cap C=\left\{G_{1} G_{2}\right\} \\ &P(A)=2 \\ &P(B)=2 \end{aligned}

  1. Required probability P(A \mid B)=\frac{P(A \cap B)}{p(B)}=\frac{1}{2}
  2. Required probability  P(A \mid C)=\frac{P(A \cap C)}{p(C)}=\frac{1}{3}

 

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