There are three events `E_1, E_2` and `E_3` one of which must, and only one can happen. The odds are 7 to 4 against `E_1` and 5 to 3 against `E_2`. Find odds against `E_3`.

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.

True or false Two events E_1 and E_2 are said to be mutaully exclusive iff E_1capE_2=phi

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.

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.

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?

Of the three independent events E_(1),E_(2),and E_(3), the probability that only E_(1) occurs is alpha only E_(2) occurs is beta, and only E_(3) occurs is gamma. Let the probability p that none of events E_(1),E_(2), or E_(3) occurs satisfy the equations (alpha-2beta)p=alpha betaand (beta-3gamma)p=2betagamma. All the given probabilities are assumed to lie in the interval (0,1). Then ("Probability of occurrence of"E_(1))/("Probability of occurence of"E_(3))=

If E_1 and E_2 are two independent events associated with an experiment, then show that E_1^c and E_2^c are alos independent.

A series of concentric ellipses E_1,E_2, E_3..., E_n are drawn such that E touches the extremities of the major axis of E_(n-1) , and the foci of E_n coincide with the extremities of minor axis of E_(n-1) If the eccentricity of the ellipses is independent of n, then the value of the eccentricity, is

A coin is tossed thrice and all the eight outcomes are assumed to be equally likely. In which of the following cases are the events E_1 and E_2 independent? E_1 : 'the number of heads is odd E_2 : 'the number of tail is odd'.