Question

Example 46: The contents of urns I, II and III are as follows: 2
white, 3 black and 4 red balls; 3 white, 2 black and 2 red balls and
4 white, 1 black and 3 red balls. An urn is chosen at random and
two balls are drawn. They happen to be white and red. What is the
probability that they come from urs I, II or III?​

Answer 1

Question:-The contents of urns i, ii, iii are as follows: 1) 1 white, 2 black and 3 red balls 2) 2 white, 1 black and 1 red balls 3) 4 white, 5 black and 3 red balls one urn is chosen at random and two balls drawn. They happen to be a white and a red. What is the probability that they come from: a. Urn i b. Urn ii or iii

Answer:

Given :-

White Black Red

1) 1 2 3

2) 2 1 1

3) 4 5 3

To find :-

They happen to be a white and a red. What is the probability that they come from: a. Urn i b. Urn ii

Solution :-

Let A be the event that the two balls taken from selected urn is red and white.

P(E1)=P(E2)=P(E3)=1/3

P(A/E1)=(3×1)/6C2

=3/(6!/4!2!)

=3/{(6×5×4!)/4!2}

=6/30

=1/5

P(A/E2)=(1×2)/4C2

=4/12

=1/3

P(A/E3)=(3×4)/12C2

=2/11

P(E1/A)=33/118

P(E2/A)=55/118

P(E3/A)=30/118.