Please provide the solution for this problem

#1

help me with this problem

#2

Hey @muditarya31, can you please specify the question number which you are not able to understand ?

Thanks !

#3

ques no. 3. The one in which we need to compute the probability.

#4

Sure. The question says :

Two urns 1 and 2 contains 3 red & 4 black balls, 2 red & 5 black balls respectively. A ball is transferred from urn 1 to urn 2 and then a ball is drawn from urn 2. If the ball is found to be red find the probability that the ball transferred from urn 1 is black.

Now what we can make out from the question is that urn 1 contains 3 red balls and 4 black balls whereas urn 2 contains 2 red balls and 5 black balls right ? The question says that 1 ball is transferred from urn 1 to urn 2 and then a ball is drawn from urn 2. So there can be two cases.

Case 1 : The ball transferred from urn 1 to urn 2 is a black ball.

Now the probability for drawing a black ball from Urn 1 is 4/7 initially.

After the transfer the status of urn 2 will become :

urn 2 will have 2 red balls and 6 black balls

Now the question says that the final ball drawn from urn 2 comes out to be red. Probability of drawing a red ball from urn 2 now will be : 2/2+6 = 2/8 = 1/4
So total probability of case 1 will be : 4/7 * 1/4 = 1/7

Case 2 : The ball transferred from urn 1 to urn 2 is a red ball.

The probability of drawing a red ball from urn 1 is 3/7 initially.

After the transfer the status of urn 2 will become :

urn 2 will contain 3 red balls and 5 black balls

Now the question says that the final ball drawn from urn 2 comes out to be red. Probability of drawing a red ball from urn 2 now will be : 3/3+5 = 3/8
So total probability for case 2 to happen will be : 3/7 * 3/8 = 9/56

We need to find out the probability of case 1 to take place provided both of these cases can occur. So final answer would be P(Case 1) / P(Case 1) + P(Case 2) which is equal to
(1/7) / (1/7 + 9/56)
which is equal to 8/17.

I hope this explains you the solution well and clears your doubt.
Please mark the doubt as resolved in your doubts section :+1:
Happy Learning ! :slightly_smiling_face:

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#5

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