Question

An urn contains 10 wte and 3 black balls. Another urn contains 3 wte and 5 black balls. Two balls are drawn from the first urn and put into the second urn and then a ball is drawn from the second urn. Find the probability that it is a wte ball.

Answer 1

Let E1, E2, E3 and A be the event defined as follows


E1 = Two white balls are transferred from the first urn to the second urn

E2 = Two black balls are transferred from the first urn to the second urn


E3 = One black and one white ball are transferred from the first urn to the second


A = a white ball is drawn from the second urn


Since first urn contains 10 white and 3 black balls,

[Please refer the above attachment 1 ]
If E1 has already occurred then second urn containing 5 white and 5 black balls so,

p(a/e1)=5/10



If E2 has already occurred then second urn contains 3 white and 7 black balls so,

p(a/e2)= 3/10


If E3 has already occurred then the second urn contains 4 white and 6 black balls so,

p(a/e3)=4/10
finally

by law of probability
[please refer to the above attachment 2]

thank you...
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