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  • Provide solution for RD Sharma Maths Class 12 Chapter 30 Probability Exercise 30.3 question 8 sub question (iii).

Provide solution for RD Sharma Maths Class 12 Chapter 30 Probability Exercise 30.3 question 8 sub question (iii).

Answers (1)

Answer : =P\left(\frac{A}{B}\right)=\frac{P(A \cap B)}{P(B)}=\frac{6}{7}

Hint: \text{Probability}=\frac{\text{No. of outcomes}}{\text{Total no.of Outcomes }}

Given,

            A=At most two tails

            B=At least one tail

Solution:

Clearly,

\begin{aligned} &S=\{(H H H),(H H T),(H H T),(T T H),(T T T),(H T H),(T H H),(T T H)\} \\ &A=\{(\pi H),(T H H),(\mathrm{HHT}),(T H T),(\mathrm{HHT}),(\mathrm{HTT}),(\mathrm{HHH})\} \\ &\mathrm{B}=\{(\mathrm{TT}),(\mathrm{TH}),(\mathrm{THH}),(\mathrm{HHT}),(\mathrm{THT}),(\mathrm{HHT}),(\mathrm{HTT})\} \end{aligned}

Now, \mathrm{A} \cap \mathrm{B}=\{(\mathrm{TTH}),(\mathrm{THH}),(\mathrm{HHT}),(\mathrm{HTT})\}

P(A) = 7
P(B) = 7

Required Probability =P\left(\frac{A}{B}\right)=\frac{P(A \cap B)}{P(B)}=\frac{6}{7}

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