CBSE Class 12-science Answered
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 | 19 Aug, 2016, 23:37: PM
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) =
.
![](https://images.topperlearning.com/topper/questions/12855_image012.gif)
P(B/A2) is probability of event that the urn contains 2 white balls and both have been drawn.
![](https://images.topperlearning.com/topper/questions/12855_image013.gif)
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](https://images.topperlearning.com/topper/tinymce/cache/c58071834ff6de345b970f3c43c37291.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/c58071834ff6de345b970f3c43c37291.png)
By Bayes’ theorem,
![](https://images.topperlearning.com/topper/questions/12855_image015.gif)
Answered by | 20 Aug, 2016, 01:37: AM
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