Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Explain solution RD Sharma class 12 chapter Probability exercise 30.7 question 8 maths

Explain solution RD Sharma class 12 chapter Probability exercise 30.7 question 8 maths

Answers (1)

Answer:

 i)\: \frac{12}{17}, \quad ii)\: \frac{5}{17}

Hint:

 Use Baye’s theorem.

Given:

 A letter is known to have come either from LONDON or CLIFTON on the envelope just two consecutive letter on are visible what is probability that letter has come from (i) LONDON (ii) CLIFTON

Solution:

Let E1 is event that letter come from LONDON and E2 is event that letter come from CLIFTON.

Thus

P(E_1)=P(E_2)=\frac{1}{2}

Let A be event come 2 consecutive letter on envelope are ON.

Then

P\left ( \frac{A}{E_1} \right )=\frac{2}{5}

And

P\left ( \frac{A}{E_2} \right )=\frac{1}{6}

Now

Using Baye’s theorem we get

\begin{aligned} &P\left (\frac{E_1}{A} \right )=\frac{P(E_1).P\left ( \frac{A}{E_1} \right )}{P(E_1)\times P\left ( \frac{A}{E_1} \right )+P(E_2)\times P\left ( \frac{A}{E_2} \right )}\\ &P\left (\frac{E_1}{A} \right )=\frac{{\frac{1}{2}\times \frac{2}{5} }}{\frac{1}{2}\times \frac{2}{5}+\frac{1}{2}\times \frac{1}{6}}\\ &=\frac{12}{17} \end{aligned}

i. Now

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 )}\\ &P\left (\frac{E_2}{A} \right )=\frac{{\frac{1}{2}\times \frac{1}{6} }}{\frac{1}{2}\times \frac{2}{5}+\frac{1}{2}\times \frac{1}{6}}\\ &=\frac{\frac{1}{6}}{\frac{12+5}{30}}\\ &=\frac{1}{6}\times \frac{30}{17}\\ &=\frac{5}{17} \end{aligned}

Posted by

Gurleen Kaur

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

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14
anam-khan

CBSE Board Exams 2025: Online portal for availing exemptions by CWSN students opens
anam-khan

Board Exams: States agree to equivalence; no question paper ‘jumbling’ from next year, says PARAKH CEO

Latest Question