Correct Answer - A::B::C
Since ,
1+3p
3
,
1-p
4
and
1-2p
2
are the probability of mutually exclusive events .
∴
1+3p
3
+
1-p
4
+
1-2P
2
≤1
⇒4+12P+3-3P+6-12P≤12
⇒ 13-3p≤12
⇒ p≥
1
3
...
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
