An urn contains three white, six red and four black balls. Two balls are selected at random. What is the probability that one ball is red and other is white, given that they are of different colour ?

Options

A. `(2)/(3)`
B. `(1)/(3)`
C. `(1)/(2)`
D. none of these

Answer

B

Explanation

`(b)` Let `A`= event that balls are of different colors
`B=` event that one ball is red and other is white
`P((B)/(A))=(P(AnnB))/(P(A))`
`=(("^(6)C_(1)xx^(3)C_(1))/('^(13)C_(2)))/(('^(3)C_(1)xx^(6)C_(1)+^(3)C_(1)xx^(4)C_(1)+^(4)C_(1)xx^(6)C_(1))/('^(13)C_(2)))`
`=(6xx3)/(6xx3+3xx4+4xx6)=(1)/(3)`