GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
124 views
Suppose a box contains three cards, one with both sides white, one with both sides black, and one with one side white and the other side black. If you pick a card at random, and the side facing you is white, then the probability that the other side is white is $1/2$.
asked in Probability by Veteran (39.7k points) 256 1308 1941 | 124 views

2 Answers

+3 votes

1 card both side white

1 card both side black

1 card 1 side white 1side black

from these 3 cards probability of choosing any one card is 1/3

Now while 1 side of the card is white , then the probability of other side also white

By Baye's theorem

1/3*P(W) /(1/3*P(W) +1/3 *P(B))

=(1/3*1/2) /(((1/3)*(1/2))+((1/3)*(1/2)))

=1/2 [Proved]

 

answered by Veteran (65.1k points) 35 222 625
How's the Bayes formula applied here? - the terms are not clear.
No sir I think it is clear

Because we already know one side is white

Then probability of other side white

It is a conditional probability :)
yes, but that is intuition. We know only 2 coins are there with at least one face white. Try applying Bayes formula properly, you should not get 1/2 and this is a common mistake everyone makes in conditional probability.

@Srestha I think approach is correct. But wrong values substituted. Can u pls recheck once?

It is asked - Prob of other side white when one side is white

Nothing but using bayes theorem to identify White appeared what is probablity that source is unfair card with both sides white.

(1/3)(1) / (  (1/3)(1) + (1/3)(0) + (1/3)(1/2) ) = 2/3

@srestha

@Arjun Sir,

I think, the solution of @yg92 is correct.

just check it.

since in the question they have mentioned that one side of the card is white and they are willing to know or the favourable case is white on both the side.

Hence, the numerator should be (1/3) * 1, because 1/3 is for choosing the card and 1 as we know that its both faces are white, hence probability of white on that card will be 1 and that is what we want.

And the denomenator will the total probability.

@yg92

" the side facing you is white " is mentioned in question. Not both side should be white.

@ Shubhanshu

no where mentioned both side should be white

0 votes
Pls correct me if i am wrong

 

Given - selected white face  = 1/3*1 + 1/3*1/2

To calculate other side probability is white is 1/2 => 1/3*1/2  /  (1/3*1 + 1/3*1/2)  = > 1/3
answered by Active (1.6k points) 3 6 14


Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
Top Users Oct 2017
  1. Arjun

    23398 Points

  2. Bikram

    17078 Points

  3. Habibkhan

    8264 Points

  4. srestha

    6296 Points

  5. Debashish Deka

    5438 Points

  6. jothee

    4978 Points

  7. Sachin Mittal 1

    4772 Points

  8. joshi_nitish

    4348 Points

  9. sushmita

    3964 Points

  10. Rishi yadav

    3804 Points


Recent Badges

Notable Question KISHALAY DAS
Notable Question sh!va
Notable Question abhijeetbzu
Great Question jothee
Popular Question rahul sharma 5
Nice Question mohit kumar 5
Notable Question rishu_darkshadow
Nice Comment Pranay Datta 1
Copy Editor Shivansh Gupta
Nice Comment KULDEEP SINGH 2
27,324 questions
35,176 answers
84,108 comments
33,279 users