Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • There are three coins. One is a two-headed coin, another is a biased coin that comes up heads 75% of the time and the third is an unbiased coin. One of the three coins is chosen at random and tossed. If it shows heads, what is the probability that it i

There are three coins. One is a two-headed coin, another is a biased coin that comes up heads 75% of the time and the third is an unbiased coin. One of the three coins is chosen at random and tossed. If it shows heads, what is the probability that it is a two- headed coin?

 

 

 

 

 
 
 
 
 

Answers (1)

Given there are 3 coins 

Let, 

E1 = coin is two headed

E2 = biased coin 

E3 = unbiased coin 

A = Shows only head

Here

 P(E_1)=P(E_2)=P(E_3)=\frac{1}{3} \\ then , \: P(\frac{A}{E_1})=1 \: \: \: \: \: P\left ( \frac{A}{E_2} \right )= \frac{1}{2} \\ P\left ( \frac{A}{E_2} \right )= \frac{75}{100}=\frac{3}{4}(given)

Now the probability of 2 headed coin

P(E_1/A)= \frac{P(E_1)P(A/E_1)}{P(E_1)\times P(A/E_1)+P(E_2)\times P(A/E_2)+P(E_3)\times P(A/E_3)}\\ \frac{\frac{1}{3}\times 1}{\frac{1}{3}\times 1 +\frac{1}{3}\times \frac{3}{4}+ \frac{1}{3}\times \frac{1}{2}}=\frac{1}{\frac{4+3+2}{4}}= \frac {4 }{9}

Posted by

Ravindra Pindel

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 Board exams twice a year from 2025, no plan for semesters: MoE
anam-khan

CBSE Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years

Latest Question