An urn contains 6 white and 4 black balls. A fair
die is rolled and that number of balls we chosen from the urn. Find the
probability that the balls selected are white.
Text Solution
Verified by Experts
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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