A die is rolled and showing any number is directly proportional to that number. If prime number appears then a ball is chosen from urn `A` containing 2 white and 3 black balls otherwise a ball is chosen from urn `B` containing 3 white and 2 black balls Then.
The probability of drawing a black ball is

Options

A. `53/105`
B. `52/105`
C. `49/105`
D. `51/105`

Answer

B

Explanation

`P(i)alphai`
`P(i)=Ki`
`P(1)=K,P(2)=2K,…….P(6)=6K`
`K=2K+…+6K=1`
`K(1+2+…+6)=1`
`K+1/21`
`P(1)=1/21, P(2)=2/21,……P(6)=6/21`
`P` (Prime number) `=2/21+3/21+5/21=10/21`
`P`(not prime) `=11/21`
`P(B)=10/21xx3/5+11/21xx2/5=52/105`
`P(w)=10/21xx2/5+11/21xx3/5=53/105`
`P((urnB)/w)=(33/105)/(53/105)=33/53`