If `p` is the probability that a man aged `x` will die in a year, then the probability that out of `n` men `A_1,A_2, A_n` each aged `x ,A_1` will die in an year and be the first to die is a.`1-(1-p)^n` b. `(1-p)^n` c. `1//n[1-(1-p)^n]` d. `1//n(1-p)^n`

An unbiased die is such that probability of number n appearing is proportional to n^2(n=1,2,3,4,5,6)dot The die is rolled twice, giving the numbers aa n db . Then find the probability that a< b

If x ,1,a n dz are in A.P. and x ,2,a n dz are in G.P., then prove that x ,a n d4,z are in H.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 ^n P_r=^n P_(r+1)a n d^n C_r=^n C_(r-1,) then the value of n+r is.

Let the sequence a_n be defined as follows: a_1 = 1, a_n = a_(n - 1) + 2 for n ge 2 . Find first five terms and write corresponding series

If p is the first of the n arithmetic means between two numbers and q be the first on n harmonic means between the same numbers. Then, show that q does not lie between p and ((n+1)/(n-1))^2 p.

Find the first 6 terms of the sequence given by a_1=1, a_n=a_(n-1)+2 , n ge 2

Ea n dF are two independent events. The probability that both Ea n dF happen is 1/12 and the probability that neither Ea n dF happens is 1/2 . Then, A) P(E)=1//3, P(F)=1//4 B) P(E)=1//4, P(F)=1//3 C) P(E)=1//6, P(F)=1//2 D) P(E)=1//2, P(F)=1//6

If f(x) =(p-x^n)^(1/n) , p >0 and n is a positive integer then f[f(x)] is equal to

Two players P_1a n dP_2 play a series of 2n games. Each game can result in either a win or a loss for P_1dot the total number of ways in which P_1 can win the series of these games is equal to a. 1/2(2^(2n)-^ "^(2n)C_n) b. 1/2(2^(2n)-2xx^"^(2n)C_n) c. 1/2(2^n-^"^(2n)C_n) d. 1/2(2^n-2xx^"^(2n)C_n)