One ticket is drawn from a purse containing four tickets with numbers 223, 133, 212, 322. Let $A_i$ be the event that i$^{th}$ digit of the number on drawn ticket is 2. Then which of the following events are independent ?

A. $A_1$ and $A_2$

B. $A_2$ and $A_3$

C. $A_1$ and $A_3$

D. $A_1$, $A_2$ and $A_3$

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If the mean and variance of a binomially distributed random variable X are 4 and 2 respectively, then $P(X = 2)$ is equal to

A die is thrown and a coin is tossed. The probability that the outcome will be a number greater than 4 or a head or both is

If A and B are independent events such that $P(A)=\dfrac{1}{2}$, $P(A\cup B)=\dfrac{3}{5}$ and $P(B)=p$, then value of p is:

Let $F(z)$ be the cumulative density function of the standard normal variate $z$, then which of the following are correct?

(A) $F(z) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^z e^{-\frac{z^2}{2}} dz$, $-\infty < z < \infty$

(B) $F(-z) = 1 - F(z)$

(C) $F(0) = 0$

(D) $F(\infty) = 1$

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Let A and B are two events associated to a random experiment, then

Match the LIST-I with LIST-II

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If A, B and C are three independent events such that P(A)=P(B)=P(C)=x, then P(at least two of A, B, C occur) =