Question

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.

Answer 1

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`