A bag contains 5 balls. Two balls are drawn and are found to be white. What is the probability that all the balls are white?

Answer

`1//2`

Explanation

Let `A_(i)(i=1,2,3,4)` be th eevent that the urn contains `2,3,4 or5` white balls and E the event that two white balls are drawn. Since the four events `A_(1),A_(2),A_(3),A_(4)` are equally likely, therefore `P(A_(i))=1//4,i=1,2,3,4.` Now, the probability tyhat the urn contains 2 white balls and both have been drawn is
`P(E//A_(1))=(""^(2)C_(2))/(""^(5)C_(2))=1/10`
Similarly, `P(E//A_(2))=(""^(3)C_(2))/(""^(5)C_(2))=3/10,`
`P(E//A_(3))=(""^(4)C_(2))/(""^(5)C_(2))=3/5`
`P(E//A_(4))=(""^(5)C_(2))/(""^(5)C_(2))=1`
Hence, the required probability is
`P(A_(4)//E)=(P(A_(4))P(E//A_(2)))/(underset(i=1)overset(4)sumP(A_(i))P(E//A_(i)))`
`=(1/4xx1)/(1/4((1)/(10)+(3)/(10)+(3)/(5)+1))=1/2`