34 votes 34 votes You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is $\dfrac{1}{4}$ $\dfrac{1}{3}$ $\dfrac{1}{2}$ $\dfrac{2}{3}$ Quantitative Aptitude gate2014-ec-1 quantitative-aptitude probability conditional-probability + – makhdoom ghaya asked Mar 18, 2016 recategorized Apr 25, 2021 by Lakshman Bhaiya makhdoom ghaya 10.1k views answer comment Share Follow See all 5 Comments See all 5 5 Comments reply Show 2 previous comments srestha commented Oct 23, 2019 reply Follow Share This answer is more logical 0 votes 0 votes Overflow04 commented Oct 26, 2022 reply Follow Share @smsubham @Abhrajyoti00 I am not able to understand how $E_{1} \bigcap E_{2} = (3,H)$ 0 votes 0 votes Abhrajyoti00 commented Oct 26, 2022 reply Follow Share @GateOverflow04 Always solve such problem using Tree Method. It’s very easy. Conditional Probability is confusing at times.The answer to your doubt : $E_{1} \bigcap E_{2} = (3,H)$ because only incase of Coin 3 we will get the reqd event when Toss comes Head and the other face is Tail. And it's $H$ because we need to find it's probability. 2 votes 2 votes Please log in or register to add a comment.
0 votes 0 votes ans is option B.1/3 amollawate answered Mar 18, 2016 amollawate comment Share Follow See all 3 Comments See all 3 3 Comments reply Siddhi Viradiya commented Jul 20, 2016 reply Follow Share i am confused ..my answer is also 1/3 ..but in discussion of some sites like m4maths and others some people written that answer is 1/2.so can anyone explain this with proper explanation. http://www.m4maths.com/82342-You-are-given-three-coins-one-has-heads-on-both-faces-the-second-has-tails-on-both-faces-and-the.html 0 votes 0 votes Pankaj Joshi commented Dec 11, 2016 i reshown by Pankaj Joshi Dec 11, 2016 reply Follow Share check my answer 0 votes 0 votes Rishi yadav commented Oct 17, 2017 reply Follow Share No answer is 1/3 because Question asked about we have a head and find probability for other face which should be tail so Unfair coin doesn't have tail at other side so 0 we don't TT type unfair coin because it show Tail so no need to worry about it so simply 1 votes 1 votes Please log in or register to add a comment.
0 votes 0 votes B. 1/3 . Only one coin has the head on one face and tail on another and we can select one coin from 3 coins in 3 ways. So, probability is favorable cases (one in this case) divided by total cases i.e 3. Vishu Nair answered Jun 13, 2018 Vishu Nair comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes This illustration may help and note here we have equal probablity for choosing fair, unfair H & T coin as 1/3 each. Asim Siddiqui 4 answered Dec 4, 2020 Asim Siddiqui 4 comment Share Follow See all 0 reply Please log in or register to add a comment.