An urn contains five balls. Two balls are drawn and found to be white. Find the probability that all the balls are white.  

Asked by Topperlearning User | 19th Aug, 2016, 11:37: PM

Expert Answer:

Let Ai ( i = 2, 3, 4, 5) be the event that urn contains 2, 3, 4, 5 white balls and let B be the event that two white balls have been drawn then we have to find P (A5/B).

Since the four events A2, A3, A4 and A5 are equally likely we have
P (A2) = P (A3) = P (A4) = P(A5) = .
P(B/A2) is probability of event that the urn contains 2 white balls and both have been drawn.
Similarly,P left parenthesis B divided by A subscript 3 right parenthesis equals fraction numerator C presuperscript 3 subscript 2 over denominator C presuperscript 5 subscript 2 end fraction equals 3 over 10 comma space P left parenthesis B divided by A subscript 4 right parenthesis equals fraction numerator C presuperscript 4 subscript 2 over denominator C presuperscript 5 subscript 2 end fraction equals 3 over 5 comma space P left parenthesis B divided by A subscript 5 right parenthesis equals fraction numerator C presuperscript 5 subscript 2 over denominator C presuperscript 5 subscript 2 end fraction equals 1
By Bayes’ theorem,

Answered by  | 20th Aug, 2016, 01:37: AM