A die is thrown 6 times. If getting an odd number is a success, then the probability of at least 5 successes is

There are 50 telephone lines in an exchange. The probability that any one of them will be busy is 0.1, then the probability that all the lines are busy?

Bag I contains 3 black and 2 white balls. Bag II contains 2 black and 4 white balls. A bag is selected at random and then a ball is drawn from it. The probability that the ball drawn is black is:

The probabilities of occurrence of two events E and F are 0.25 and 0.50 respectively. The probability of their simultaneous occurrence is 0.14. The probability that neither E nor F occurs is

A player participates in 3 matches against three teams T₁, T₂ and T₃.The probability of winning a match against teams T₁, T₂ and T₃ are 0.2, 0.3 and 0.9 respectively. If 'wins' can be regarded as independent events, then the probability that he

(A) wins all the 3 matches is 0.054

(B) wins no match is 0.054

(C) wins exactly two matches is 0.348

(D) wins exactly one match is 0.542

Choose the correct answer from the options given below:

The random variable $X$ has a probability distribution

$P(X=x) = \begin{cases} 5k, & x=0 \\ 2k, & x=1 \\ 3k, & x=2 \\ 0, & \text{otherwise.} \end{cases}$

Then, the value of $E(X)$ is :

Two dice are thrown simultaneously. If X denotes the number of sixes, then the variance of X is: