Question

Each of the n urn contains a white and b black balls. One ball is transferred from the first urn into the second, then one ball from the latter into third and so on. Finally, one ball is taken from the last urn, what is the probability of its being white?
There is a series of n urns. In the ith urn there are i white and (n-i) black balls, i =1,2,3,...,n. One urn is chosen at random and 2 balls are drawn from it. Both turn out to be white. What is the probability that the jth urn was chosen, where j is a particular number between 3 and n?

Answer 1

Answer:

Answer

Correct option is

A

1

Urns

I

1W,2B

II

2W,1B

III

2W,2B

There are four possibilities in transference.

(i) W ball goes from I to II; and W goes from II to III So probability of drawing a W ball from urn III

=

3

1

×

4

3

×

5

3

×=

60

9

(ii) W goes from I to II, B goes from II to III then prob. of W from III

=

3

1

×

4

1

×

5

2

×=

60

2

(iii) B goes from I to II. W goes from II to III, then prob. of W from III

=

3

2

×

4

2

×

5

3

×=

60

12

(iv) B goes from I to II, B goes from II to III, then prob. of W from III

=

3

2

×

4

2

×

5

2

×=

60

8

These are mutually exclusive events, so required prob. = sum of these

=

60

9

+

60

2

+

60

12

+

60

8

=

60

31

Hence, k=1