Please wait...
1800-212-7858 (Toll Free)
9:00am - 8:00pm IST all days

or

Thanks, You will receive a call shortly.
Customer Support

You are very important to us

For any content/service related issues please contact on this toll free number

022-62211530

Mon to Sat - 11 AM to 8 PM

A bag contains 4 balls. Two balls are drawn at random & are found to be black. What is the probability that all the balls are black?

Asked by adityasood 27th January 2011, 12:00 AM
Answered by Expert
Answer:
Dear Student,
Here is the solution:

We need to compute P(all balls black | drew 2 black balls).
This is a conditional probability so we use Bayes Law.
P(A | B) = P(B | A)  x  P(A)/ P(B).

Where A = all balls black
B = draw 2 black balls

P(B) is not given. I will assume there are 3 possible worlds: 4 blacks, 3 blacks and 1 non black,
and 2 blacks and 2 non-black. I need to also know the probabilities for each of these worlds. I will assume they are equal, the standard assumption if no information is given.

P(B) = P(B| 4black) x P(4black) +P(B| 3black, 1non-black) x P(3black, 1 non-black) + P(B | 2black,2 non-black).

P(B|4black) = 1
P(4black) = 1/3 = P(3black and 2 non) = P(2black and 2 non)

P(B | 3black and 1 non) = 3/4 x 2/3 = 1/2

P(B | 2black and 1 non) = 2/4 x 1/3 = 1/6

Putting this all together with Bayes:
P(4black in bag | drew 2 black) = 1 x 1/3/ ( 1x1/3 + 1/2x1/3 + 1/6x1/3) = 3/5
 
Regards
 
Team Topperlearning
Answered by Expert 7th February 2011, 5:04 PM
Rate this answer
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10

You have rated this answer /10

Your answer has been posted successfully!

Free related questions

17th June 2016, 10:14 AM
17th June 2016, 12:17 PM
17th June 2016, 11:04 AM
17th June 2016, 11:47 AM
23rd June 2016, 5:44 PM

Chat with us on WhatsApp