Two cards are drawn successively with replacement from a well shuffled pack of 52 playing cards. Which of the following is correct probability distribution of number of Queens(X) as $\binom{X}{P(X)}$?

If a fair coin is tossed 10 times, then the probability of obtaining at least one head is :

If A and B are two independent events such that P(A) = 1/3, $P(A\cup B) = 3/5$ and P(B) = p, then which of the following are true?

(A) The value of p is $\frac{2}{5}$

(B) $P(A\cap B) = \frac{2}{15}$

(C) $P(B/A) = \frac{1}{3}$

(D) $P(A/B) = \frac{3}{5}$

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Let X denotes the number of hours a person uses a mobile and the probability distribution of X is as

Then the value of K is

The probability distribution function of a normal variate with mean $\mu$ and variance $\sigma^2$ is given by:

$f(x) = \frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{1}{2}(\frac{x-\mu}{\sigma})^2}$, $-\infty < x < \infty$, $-\infty < \mu < \infty$, $\sigma > 0$

If $y = f(x)$ be the normal probability curve, then which of the following is correct?

(A) The normal curve is symmetrical about the line $x = \mu$.

(B) Mean, median and mode of the distribution coincide.

(C) Y- axis is an asymptote to the normal curve.

(D) If x increases numerically, $f(x)$ decreases rapidly.

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Let E and F be two events such that $P(E) = \frac{1}{3}$, $P(F) = \frac{1}{4}$ and $P(E \cap F) = \frac{1}{5}$. Then the value of $P(F|E)$ is equal to

If A and B are two independent events such that P(A) = 0.5, P(B) = 0.3 then

Match the LIST-I with LIST-II

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