A problem is given to 3 students A,B and C, whose probabilities of solving are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively, then

(A). P(Problem solved) = $\frac{3}{4}$

(B). P(Problem not solved) = $\frac{1}{4}$

(C). P(Problem solved by exactly one student) = $\frac{7}{24}$

(D). P(Problem solved by at least 2 students) = $\frac{17}{24}$

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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:

Let x denotes the number of heads in a simultaneous toss of three coins, then $P(0 < x \leq 3)$

Let the random variable X represent the positive difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. Then probability $P(X \leq 3)$ is equal to

The random variable X can take values 0, 1, 2. If $P(X=0)=P(X=1)=\alpha$, and $E(X^2)=E(X)$, then which of the following are correct?

(A) $E(X) = 2-3\alpha$

(B) $E(X^2) = 4+7\alpha$

(C) $\alpha = \frac{1}{2}$

(D) $\alpha = \frac{1}{5}$

Choose the correct answer from the options given below:

What is the mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on 1 face?

Let A and B be two independent events. Then which of following statements is not true?