If `(1 + 3p)/(3), (1 - p)/(4)` and `(1 - 2p)/(2)` are the probabilities of three mutually exclusive events, then find the set of all values of p.

Answer

A, B, C

Explanation

Since `,(1+3p)/(3),(1-p)/(4)and (1-2p)/(2)` are the probability of mutually exclusive events .
` therefore " " (1+3p)/(3)+(1-p)/(4)+ (1-2P)/(2) le 1`
`rArr 4+12P+3 -3P+6 -12 P le 12 `
`rArr " " 13-3p le 12 `
`rArr " " p ge 1/3 .....(i)`
and `0 le (1+3p)/(3) le 1, 0 le (1-p)/(4) le 1, 0 le (1-2p)/(2) le 1`
`rArr 0 le 1 + 3p le 3,0 le 1- p le 4, 0 le 1 -2p le 2 `
` rArr -1/3 le p le 2/3 , 1 ge p ge -3 , 1/2 ge p ge - 1/2`
From Eqs (i) and (ii) `1//3 le p le 1//2`