Probability

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

The variance of the following probability distribution is,

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

If $X$ is a.r.v. with c.d.f $F(x)$ and its probability distribution is given by

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
...

The odds in favour of getting sum multiple of 3 , when pair of dice are thrown is

If the p.m.f of a. r.v. \(X\) is given by
\(P(X=x)=\frac{{ }^5 C_x}{2^5}\)
if \(x=0,1,2, \ldots \ldots . .5=0\),
0 , otherwise,
then which of the following is not true?

The p.d.f of c.r.v \(X\) is given by \(f(x)=\frac{x+2}{18}\), if $$-2

The letters of the word 'LOGARITHM' are arranged at random. The probability that arrangement starts with vowel and end with consonant is

The probability that bomb will miss the target is 0.2. Then, the probability that out of 10 bombs dropped exactly 2 will hit the target is

The pdf of a continuous r.v. \(X\) is given by \(f(x)=\frac{x}{8}, 0 < x < 4=0\), otherwise, then \(P(X \leq 2)\) is

Out of 100 people selected at random, 10 have common cold. If five persons selected at random from the group, then the probability that at most one person will have common cold is

The odds in favour of drawing a king from a pack of 52 playing cards is

If a die is thrown at random, then the expectation of the number on it is

A player tosses 2 fair coins. He wins Rs. 5 if 2 heads appear, Rs. 2 If 1 head appear and Rs. 1 if no head appears, then variance of his winning amount is

$$\begin{aligned} &\text { The pdf of a random variable } X \text { is }\\ &\begin{aligned} f(x) & =3\left(1-2 x^2\right), & & 0< x<1 \\ & =0 & & \text { otherwise } \end{aligned} \end{aligned}$$
The $P\left(\frac{1}{4}< x<\frac{1}{3}\right...

The probability that three cards drawn from a pack of 52 cards, all are red is

Let $X$ be the number of successes in ' $n$ ' independent Bernoulli trials with probability of success $p=\frac{3}{4}$. The least value of ' $n$ ' so that $P(X \geq 1) \geq 0.9375$ is ......

If the c.d.f (cumulative distribution function) is given by $F(x)=\frac{x-25}{10}$, then $P(27 \leq x \leq 33)=\ldots \ldots$

A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour is ...........

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 probability that atleast 5 of them will be solved is

A random variable X has following probability distribution

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padd...

If three dices are thrown then the probability that the sum of the numbers on their uppermost faces to be atleast 5 is

The p.d.f of a random variable $x$ is given by
$$\begin{aligned} & f(x)=\frac{1}{4 a}, \quad 00) \\ & =0 \text {, otherwise } \end{aligned}$$
and $P\left(x<\frac{3 a}{2}\right)=k P\left(x>\frac{5 a}{2}\right)$ then $k=$ ..............

In a bionomial distribution, mean is 18 and variance is 12 then $p=$ ...........