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 `1-(1-p)^n` b. `(1-p)^n` c. `1//n[1-(1-p)^n]` d. `1//n(1-p)^n`

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

If p be occurrence of an event in a single trail, then show that the probability of at least one occurrence in n trials is 1-(1-p)^n .

A coin has probability p of showing head when tossed. 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 geq 3 .

Prove that, if A_1 and A_2 are two events, which are not necessarily mutually exclusive then P(A_1 uu A_2) = P(A_1) + P(A_1 nn A_2)

Determine the number of terms in a G.P., if a_1=3,a_n=96 ,a n dS_n=189.

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 a_1,a_2,.....a_n are positive real number whose product is a fixed number c, then the minimum value of a_1+a_2+......+a_(n-1)+a_n is

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 the sum of the first m terms of an A.P. is equal to the sum of either the next n terms or the next p terms, prove that, (m+n)((1)/(m)-(1)/(p)) = (m+p)((1)/(m) - (1)/(n))

A coin is tossed. If head appears a fair die is thrown three times otherwise a biased die with probability of obtaining an even number twice as that of an odd number is thrown three times. If (n_(1),n_(2),n_(3)) is an outcome, (1 le n_(1) le6) and is found to satisfy the equation i^(n_(1))+i^(n_(2))+i^(n_(3))=1 , , then the probability that a fair die was thrown is (where i=sqrt(-1))