Suppose `Aa n dB` are two events with `P(A)=0. 5a n dP(AuuB)=0. 8.` Let `P(B)=p` if `Aa n dB` are mutually exclusive and `P(B)=q` if `Aa n dB` are independent events, then the value of `q//p` is_________.

Options

A. `p=q`
B. `p=2q`
C. `2p=q`
D. `p+q=1`

Answer

C

Explanation

`(c )` `P(auuB)=P(A)+P(B)-P(AnnB)` ………`(i)`
When `A` and `B` are mutually exclusive, then `P(AnnB)=0`
`:.0.8=0.5+p`
`:.p=0.3`
When `A` and `B` are independent `P(AnnB)=P(A)*P(B)`
`:.` From `(i)` , `0.8=0.5+q-(0.5)q`
`:.0.3=(q)/(2)`
`impliesq=0.6`
`implies2p=q`