Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Explain Solution R.D. Sharma Class 12 Chapter 30 Probability Exercise 30.5 Question 36 Maths Textbook Solution.

Explain Solution R.D. Sharma Class 12 Chapter 30 Probability  Exercise 30.5 Question 36 Maths Textbook Solution.

Answers (1)

Answer:\frac{5}{17}

Hint: 1+a+a^{2}+..........=\frac{1}{1-a}

Given: A and B throw a pair of dice alternately.

A wins the game if he gets a total of 7 and B wins if he gets 10

Solution: Total of 7 on dice can be obtained in following ways:

(1,6) , (6,1) , (2,5) , (5,2) , (3,4) , (4,3)

Probability\: of\: getting\: 7=\frac{6}{36}=\frac{1}{6}

Probability of not getting 7=1-\frac{1}{6}=\frac{5}{6}

Total 10 on dice : (4,6),(6,4),(5,5)

Probability of getting 10=\frac{3}{36}=\frac{1}{12}

Probability of not getting 10=1-\frac{1}{12}=\frac{11}{12}

E=getting7,F=getting10

P(\mathrm{E})=\frac{1}{6}, P(\overline{\mathrm{E}})=\frac{5}{6}, P(\mathrm{~F})=\frac{1}{12}, P(\overline{\mathrm{F}})=\frac{11}{12}

Probabilities of getting 7 in first throw=\frac{1}{6}

\begin{aligned} &\therefore P(\text { getting } 7 \text { in third throw })=P(\bar{E}) P(\bar{F}) P(E)=\frac{5}{6} \times \frac{1}{6} \times \frac{11}{12} \\\\ &P(\text { getting } 7 \text { in fifth throw })=P(\bar{E}) P(\bar{F}) P(E)=\frac{5}{6} \times \frac{11}{12} \times \frac{1}{6} \\\\ &P(\text { winning } A)=\frac{1}{6}+\left(\frac{5}{6} \times \frac{11}{12} \times \frac{1}{6}\right)+\left(\frac{5}{6} \times \frac{11}{12} \times \frac{5}{6} \times \frac{11}{12} \times \frac{1}{6}\right)+\ldots . . \end{aligned}

\begin{aligned} &\frac{\frac{1}{6}}{1-\frac{5}{6} \times \frac{11}{12}}=\frac{12}{17} \\\\ &\therefore P(\text { winning } B)=1-P(\text { winning } A) \\\\ &=1-\frac{12}{17} \\\\ &=\frac{5}{17} \end{aligned}

Posted by

infoexpert21

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Date Sheet 2025: When to expect Class 10, 12 board exam time table?
anam-khan

CBSE introduces CCTV policy in board exams 2025; schools fixed as centres must have facility
anam-khan

CBSE gives parents, schools till October 16 to register students in Classes 9, 11

Latest Question