Let `E_1, E_2, E_3…………,E_n` be independent events with respective probability `P_1,P_2,P_3,………….,P_n` find the probability that
none of them occurs.

If A_1, A_2, …, A_n are n independent events, such that P(A_i)=(1)/(i+1), i=1, 2,…, n , then the probability that none of A_1, A_2, …, A_n occur, is

There are two independent events E_1 and E_2 and P(E_1)=0.30 , P(E_2)=0.60 find the probability that neither E_1 nor E_2 occurs.

Let E and F be two independent events. The probability that exactly one of them occurs is 11/25 and the probability if none of them occurring is 2/25 . If P(T) denotes the probability of occurrence of the event T , then

There are two independent events E_1 and E_2 and P(E_1)=0.30 , P(E_2)=0.60 find the probability that both E_1 and E_2 occur.

There are two independent events E_1 and E_2 and P(E_1)=0.30 , P(E_2)=0.60 find the probability that one and only one event happens.

There are two independent events E_1 and E_2 and P(E_1)=0.30 , P(E_2)=0.60 find the probability that at least one of E_1 and E_2 happens.

A ship is fitted with three engines E_1,E_2 and E_3 . The engines function independently of each other with respective probabilities 1/2, 1/4, and 1/4 . For the ship to be operational at least two of its engines must function. Let X denote the event that the ship is operational and let X_1, X_2 and X_3 denote, respectively, the events that the engines E_1, E_2 and E_3 are function. Which of the following is/are true?

If P(E) = 0.05, which is the probability of not E.

Let E_1 and E_2 be two independent events such that P(E_1)=rho_1 and P(E_2)=rho_2 . Describe in words, the events probabilities are rho_1rho_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, P(E)=1//3, P(F)=1//4 P(E)=1//4, P(F)=1//3 P(E)=1//6, P(F)=1//2 P(E)=1//2, P(F)=1//6