24thx
Be sure to read the problem clearly.
A bag contains 6 balls of different unknown colors. Probability for A and B speaking truth are p and q respectively. A ball is drawn and both cofirm it to be RED. What is the probability that the ball is red??
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17 Answers
62@ith_power
I had assumed that they "Confirmed it red"
means that they were asked the question whether the ball is red or not...
If that is not what you meant then infinty approach will work.
9yeah ans cums 1 only i fail to understand ur approach ith power
1Let me point out a point.
Please go through any book that gives the proof of baye's theorem on conditional probabality.
It will say that the denominator is the TOTAL PROBABILITY.
In this case the denominator is the probability that the ball IS RED in all possible case.
Now the case when both lie, it is not confirmed that the red ball is inside the bag.
So the probability of having a red ball which is counted in the TOTAL PROBABILITY is not
(1-p)(1-q).
In fact there are three cases for calculating total probability,
1.both say truth.
2.both lie and a red ball is inside the bag.
3.both lie and a red ball is not inside the bag..
Now calculate the probability...
13if they were asked
'what was the colour of the ball?'...then probability 1
'was that a red ball?'.....then probability what bhaiya told in post#2
33If They are asked individually....(one not knowing about other's answer..)
then answer would be 1
1i mean they answered "yeah! it is red." thats all. they might lie though! :D
@Rajat.- all balls are of different colors.
62Probability that it is red and both speak the truth is
pq
probability that it is not red and both speak a lie is
(1-p)(1-q)
Hence the prob that it is red given both say it is red is
\frac{pq}{pq+(1-p)(1-q)}
13i think the answer should be 1.....(!!!!!)
A and B could have tell any colour of the world(take the no. of colours to be ∞)....but they confirmed it to be red.....hence it should be red.....sounds strange...
don't know if i m takin rubbish
1I requested all to read it carefully. none heeded. :((
Anyway i again repeat we dont know the colors in the bag. that is we dont even know if there is a red ball or not.