IF ` A={1,{2,3}}`, find ` P(A) and n {P(A)}`.

Find n if : 2P( n,3) = P(n+1,3)

Find n if : P(2n, 3) = 100 P(n,2)

If M and N are events such that P(M)=1/4 , P(N)=1/2 , P(MbigcapN)=1/6 Find P(not M and not N).

If P(n,5):P(n,3)=2:1 find n

(i) If ""^(n)P_(4): ""^(n)P_(5)=1:2 , find n. (ii) If ""^(n-1)P_(3): ""^(n+1)P_(3)=5:12 , find n.

(i) If "^((n+1))P_(5) : "^(n)P_(6)=2:7 , find n (ii) If "^(n+1)P_5 : "^(n)P_5 = 3:2 ,find n.

If m = 1, n = 2 and p = -3, find the value of : 2mn^(4)-15m^(2)n+p

It is tossed n times. Let P_n denote the probability that no two (or more) consecutive heads occur. Prove that P_1 = 1,P_2 = 1 - p^2 and P_n= (1 - P) P_(n-1) + p(1 - P) P_(n-2) for all n leq 3 .

If p + 1/( p + 2 ) = 3 , find the value of ( p + 2 )^3 + 1/( p + 2 )^3