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In a Binomial distribution, the probability of getting a success is $\frac{3}{4}$ and the variance is $\frac{3}{8}$ then the probability of no success is:

Which of the following are the properties of Normal Distribution function f(x) and Normal probability curve:

(A) The probability of success remains the same in each trial and the number of trials is small in number.

(B) The curve is bell-shaped and is symmetrical about the mean.

(C) If set of n trials are repeated N times, then frequency f(r) of r successes is given by f(r) = N.p(r) = N$e^{-m\frac{m^r}{r!}}$, r=0,1,2,...

(D) As x increases numerically, f(x) decreases rapidly and the maximum value of f(x) occurs at x=μ(mean)

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The random variable X has the following probability distribution

such that E(x²) = 2E(x), then the value of b is:

The probability that in a year of the 22nd century choosen at random, there will be 53 Sundays is:

The probability distribution of a random variable x is given below.

Then the value of k is

If A and B are independent events and $P(A) = \frac{1}{2}$ $P(B) = \frac{1}{3}$, then

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If $P(A) = \frac{3}{10}$, $P(B) = \frac{2}{5}$ and $P(A \cup B) = \frac{3}{5}$ then the value of $P(B|A) + P(A|B)$ is:

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:

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. The probability distribution of number of aces is given by:

Suppose X has Poisson distribution such that $3 P(X=1) = 2 P(X=2)$ then $P(X>0)$ is:

For a Binomial distribution, B(n,p), where p+q=1, the sum and product of mean and variance are 8 and 12 respectively, when the value of n is:

A die is thrown 4 times and getting 3 is considered a success. The probability of 2 successes is:

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

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Let X denotes the number of doublets obtained in 3 throws of a pair of dice.

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Two persons A and B throw a die alternately till one of them gets a six and wins the game. If A begins, then the probabilities of winning of A and B respectively are

Consider two independent events A and B such that $P(A) = 0.3$, $P(B) = 0.6$.

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If E and F are independent events associated with an experiment, then which one of the following statements is correct?

Probability that a man speaks truth is $\frac{3}{4}$. He throws a die and reports that it is a six. The probability that it is actually a six is

The mean of the number of heads in the two tosses of a coin is

Five dice are thrown simultaneously. If the occurrence of an even number in a single dice is considered a success, then the probability of at most 3 successes is

If X is a random variable with probability distribution as given below:

Then, the variance of the distribution is

A random variable X has the following probability distribution:

then which of the following are TRUE?

(A) $k=0.1$

(B) $P(X < 1) = 0.4$

(C) $P(X < 2) = 0.7$

(D) $P(0 < X < 3) = 0.5$

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If $X$ is a random variable which can assume values $0, 1, 2, 3$ or $4$ such that $P(X = 1) = P(X = 2)$ and $3P(X = 3) = 4P(X = 4) = P(X = 0) = \frac{1}{8}$, then $P(X > 0)$ is:

A couple has 3 children each child is equally likely to be a boy or a girl. The probability that the eldest child is a girl given that they have atleast one boy is:

A letter is known to have come from either TATAPUR or from CHAKRATA. On the envelope, only two letters 'TA' are visible consecutively. The probability that the letter has come from CHAKRATA is:

Let A and B be independent events such that P (A) = 0.3 and P (B) = 0.4, then

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The probability that it will rain on any particular day is 50%. The probability that it rains only on the first 4 days of the week is:

It is known that 3% of plastic bags manufactured in a factory are defective. Using the Poisson distribution on a sample of 100 bags, the probability of at most one defective bag is:

A die is rolled in such a way that an even number is twice likely to occur as an odd number. If the die is rolled twice, then the mean of the number of perfect squares in two tosses 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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