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An urn contains 6 white and 4 black ball...

An urn contains 6 white and 4 black balls. A fair die whose faces are numbered from 1 to 6 is rolled and number of balls equal to that of the number appearing on the die is drawn from the urn at random. Find the probability that the balls selected are white.

Text Solution

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Let `A_(i)` denote the event that the number I appears on the dice and let E denote the event that only white balls are drawn.
Then `P(A_(i))=1/6"for"i=1,2..,6`
`and P(E//A_(i))=(""^(6)C_(i))/(""^(10)C_(i)),i=,2,.., 6`
Using total probability theore, required probability,
`P(E) =underset(i=1)overset(6)(sum)P(EnnA_(i))`
`=underset(i=1)overset(6)(sum)P(A_(i))P(E//A_(i))`
`=1/6[6/10+15/45+20/120+15/210+6/252+1/210]=1/5`
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