## MCQ (Single Correct Answer)

Two cards are drawn successively with replacement from a well-shuffled pack of 52 cards. Then mean of number of tens is

A fair die is tossed twice in succession. If $$\mathrm{X}$$ denotes the number of fours in two tosses, then the probability distribution of $$\mathrm{...

If $$\mathrm{A}$$ and $$\mathrm{B}$$ are two events such that $$\mathrm{P}(\mathrm{A})=\frac{1}{3}, \mathrm{P}(\mathrm{B})=\frac{1}{5}, \mathrm{P}(\ma...

Let a random variable $$\mathrm{X}$$ have a Binomial distribution with mean 8 and variance 4. If $$\mathrm{P}(\mathrm{X} \leq 2)=\frac{\mathrm{K}}{2^{...

From a lot of 20 baskets, which includes 6 defective baskets, a sample of 2 baskets is drawn at random one by one without replacement. The expected va...

Three of six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices is equilateral, equals __...

A binomial random variable $$\mathrm{X}$$ satisfies $$9. p(X=4)=p(X=2)$$ when $$n=6$$. Then $$p$$ is equal to

The three ships namely A, B and C sail from India to Africa. If the odds in favour of the ships reaching safely are $$2: 5,3: 7$$ and $$6: 11$$ respec...

If the sum of mean and variance of a Binomial Distribution is $$\frac{15}{2}$$ for 10 trials, then the variance is

In a game, 3 coins are tossed. A person is paid ₹ 7 /-, if he gets all heads or all tails; and he is supposed to pay ₹ 3 /-, if he gets one head or tw...

A fair die is tossed twice in succession. If $$\mathrm{X}$$ denotes the number of sixes in two tosses, then the probability distribution of $$\mathrm{...

For a binomial variate $$\mathrm{X}$$ with $$\mathrm{n}=6$$ if $$P(X=4)=\frac{135}{2^{12}}$$, then its variance is

The p.d.f. of a discrete random variable is defined as
$$\mathrm{f}(x)=\left\{\begin{array}{l}
\mathrm{k} x^2, 0 \leq x \leq 6 \\
0, \text { otherwise...

A player tosses 2 fair coins. He wins ₹5 if 2 heads appear, ₹ 2 if one head appears and ₹ 1 if no head appears. Then the variance of his winning amoun...

Three critics review a book. For the three critics the odds in favor of the book are $$2: 5, 3: 4$$ and $$4: 3$$ respectively. The probability that th...

A man takes a step forward with probability 0.4 and backwards with probability 0.6 . The probability that at the end of eleven steps, he is one step a...

A problem in statistics is given to three students A, B and C. Their probabilities of solving the problem are $$\frac{1}{2}, \frac{1}{3}$$ and $$\frac...

Two cards are drawn successively with replacement from a well shuffled pack of 52 cards, then mean of number of queens is

In a Binomial distribution with $$\mathrm{n}=4$$, if $$2 \mathrm{P}(\mathrm{X}=3)=3 \mathrm{P}(\mathrm{X}=2)$$, then the variance is

$$\mathrm{A}, \mathrm{B}, \mathrm{C}$$ are three events, one of which must and only one can happen. The odds in favor of $$\mathrm{A}$$ are $$4: 6$$, ...

The probability mass function of random variable X is given by
$$P[X=r]=\left\{\begin{array}{ll}
\frac{{ }^n C_r}{32}, & n, r \in \mathbb{N} \\
0, & ...

Three fair coins numbered 1 and 0 are tossed simultaneously. Then variance Var (X) of the probability distribution of random variable $$\mathrm{X}$$, ...

an urn contains 9 balls of which 3 are red, 4 are blue and 2 are green. Three balls are drawn at random from the urn. The probability that the three b...

It is observed that $$25 \%$$ of the cases related to child labour reported to the police station are solved. If 6 new cases are reported, then the pr...

In a meeting $$60 \%$$ of the members favour and $$40 \%$$ oppose a certain proposal. A member is selected at random and we take $$\mathrm{X}=0$$ if h...

A lot of 100 bulbs contains 10 defective bulbs. Five bulbs selected at random from the lot and sent to retain store, then the probability that the sto...

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

If $$\mathrm{X}$$ is a random variable with p.m.f. as follows.
$$\begin{aligned}
\mathrm{P}(\mathrm{X}=\mathrm{x}) & =\frac{5}{16}, \mathrm{x}=0,1 \\
...

The p.m.f. of a random variable X is $$\mathrm{P(X = x) = {1 \over {{2^5}}}\left( {_x^5} \right),x = 0,1,2,3,4,5}=0$$ then

The variance of the following probability distribution is,
...

If the sum of mean and variance of a binomial distribution for 5 trials is 1.8, then probability of a success is

Two unbiased dice are thrown. Then the probability that neither a doublet nor a total of 10 will appear is

Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number, is

A random variable X has the following probability distribution
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Rajesh has just bought a VCR from Maharashtra Electronics and the shop offers after sales service contract for Rs. 1000 for the next five years. Consi...

If $$X \sim B(4, p)$$ and $$P(X=0)=\frac{16}{81}$$, then $$P(X=4)=$$