Explain Solution R.D. Sharma Class 12 Chapter 30 Probability  Exercise 30.5 Question 35 Maths Textbook Solution.

Answers (1)

Answer: P\left ( Team\: A \right )=\frac{6}{11}

  P\left ( Team\: B \right )=\frac{5}{11}

The decision was fair as the two probabilities are almost equal.

Hint: You must know the rules of finding probability functions.

Given: In a hockey match, both teams scored same number of goals upto end of the game.

Solution:

P\left ( a\: six \right )=\frac{1}{6}

P\left ( not\: a\: six \right )=\frac{5}{6}

\begin{aligned} &P(\mathrm{~A} \text { wins })=P(6 \text { in first throw })+P(6 \text { in third throw })+\ldots \\ \end{aligned}

\begin{aligned} &=\frac{1}{6}+\left(\frac{5}{6} \times \frac{5}{6} \times \frac{1}{6}\right)+\ldots . . \\ &=\frac{1}{6}\left[1+\left(\frac{5}{6}\right)^{2}+\left(\frac{5}{6}\right)^{4}+\ldots\right] \\ \end{aligned}

\begin{aligned} &=\frac{1}{6}\left[\frac{1}{1-\frac{25}{36}}\right] \quad\left[1+a+a^{2}+a^{3}+\ldots=\frac{1}{1-a}\right] \\ &=\frac{1}{6} \times \frac{36}{11} \\ &=\frac{6}{11} \end{aligned}

\begin{aligned} &P(\mathrm{~B} \text { wins })=P(6 \text { in second throw })+P(6 \text { in fourth throw })+\ldots \\ \end{aligned}

\begin{aligned} &=\frac{5}{6} \times \frac{1}{6}+\left(\frac{5}{6} \times \frac{5}{6} \times \frac{5}{6} \times \frac{1}{6}\right)+\ldots . . \\\\ &=\frac{5}{36}\left[1+\left(\frac{5}{6}\right)^{2}+\left(\frac{5}{6}\right)^{4}+\ldots .\right] \\ \end{aligned}

\begin{aligned} &=\frac{5}{36}\left[\frac{1}{1-\frac{25}{36}}\right] \quad\left[1+a+a^{2}+a^{3}+\ldots=\frac{1}{1-a}\right] \\\\ &=\frac{5}{36} \times \frac{36}{11} \\\\ &=\frac{5}{11} \end{aligned}

Most Viewed Questions

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/-
Buy Now
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/-
Buy Now
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/-
Buy Now
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/-
Buy Now
NEET Foundation + Knockout NEET 2025 (Easy Installment)

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

₹ 3999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions