Please solve RD Sharma class 12 chapter Probability exercise 30.7 question 5 maths textbook solution

$\frac{8}{11}$

Hint:

Use baye’s theorem.

Given:

Suppose a girl throw a die. If she gets 1, 2 she toss a coin three times and note the number of tails. If she get 3, 4, 5, 6 she toss a coin once and note whether a head or tail is obtained. If she obtained exactly one tail, what is probability she threw 3, 4, 5, 6 with die.

Solution:

Let E1  be event that girl get 1 or 2.

Thus

$P(E_1)=\frac{2}{6}=\frac{1}{3},P(E_2)=\frac{4}{6}=\frac{2}{3},P(E_3)=\frac{3}{8}$

Let E2  be event that obtain tail. If she tossed a coin 3 time and exactly 1 tail show up then total favorable.

{ (THH), (HTH), (HHT) }=3

$P\left ( \frac{A}{E_1} \right )=\frac{3}{8}$

If she tossed the coin once and exactly 1 tail show up then total favorable.

$P\left ( \frac{A}{E_2} \right )=\frac{1}{2}$

The probability that she threw 3, 4, 5, 6 with given that she got exactly one tail or in other word

$P\left ( \frac{A}{E_2} \right )$

Using Baye’s theorem we get

\begin{aligned} &P\left (\frac{E_2}{A} \right )=\frac{P(E_2).P\left ( \frac{A}{E_2} \right )}{P(E_1)\times P\left ( \frac{A}{E_1} \right )+P(E_2)\times P\left ( \frac{A}{E_2} \right )}\\ &=\frac{{\frac{2}{3}\times \frac{1}{2} }}{\frac{1}{3}\times \frac{3}{8}+\frac{2}{3}\times \frac{1}{2}}\\ &=\frac{\frac{1}{3}}{\frac{1}{8}+\frac{1}{3}}\\ &=\frac{8}{11} \end{aligned}

Related Chapters

Preparation Products

Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 40000/-
Knockout NEET 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
NEET Foundation + Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 54999/- ₹ 42499/-
NEET Foundation + Knockout NEET 2024 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-