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A player tosses two coins if two heads appears he wins Rs. $4,$ if one head appears he wins Rs. $2$ , but if two tails appears he loses Rs. $3$ . Find the expected sum of money he wins?

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Important Questions on Probability

MEDIUM

Mathematics>Algebra>Probability>Random Variables and its Probability Distributions

A boy tosses fair coin

3

times. If he gets ₹

2 x

for

x

heads then his expected gain equals to ₹........

EASY

Mathematics>Algebra>Probability>Random Variables and its Probability Distributions

A poison variate

X

satisfies

P (X = 1) = P (X = 2),

then

P (X = 6)

is equal to

MEDIUM

Mathematics>Algebra>Probability>Random Variables and its Probability Distributions

A random variable $X$ has the following probability distribution:

$X = x_{i}$	$- 2$	$- 1$	$0$	$1$	$2$
$P (X = x_{i})$	$\frac{1}{6}$	$k$	$\frac{1}{4}$	$k$	$\frac{1}{6}$

The variance of this random variable is

MEDIUM

Mathematics>Algebra>Probability>Random Variables and its Probability Distributions

A box contains

6

pens,

2

of which are defective. Two pens are taken randomly from the box. If random variable

x :

Number of defective pens obtained, then standard deviation of

x =

MEDIUM

Mathematics>Algebra>Probability>Random Variables and its Probability Distributions

A random variable $X$ has the following probability distribution

$X$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P (X)$	$K - 1$	$3 K$	$K$	$3 K$	$3 K^{2}$	$K^{2}$	$K^{2} + K$

EASY

Mathematics>Algebra>Probability>Random Variables and its Probability Distributions

Given below is the probability distribution of discrete random variable $X$

$X = x$	$1$	$2$	$3$	$4$	$5$	$6$
$P [X = x]$	$K$	$0$	$2 K$	$5 K$	$K$	$3 K$

Then, $P [X \geq 4] =$

MEDIUM

Mathematics>Algebra>Probability>Random Variables and its Probability Distributions

A random variable

X

takes the values

0, 1, 2

. Its mean is

1.2

P (X = 0) = 0.3

, then

P (X = 1) =

MEDIUM

Mathematics>Algebra>Probability>Random Variables and its Probability Distributions

What is the mean of $f (x) = 3 x + 2$ where $x$ is a random variable with probability distribution

$X = x$	$1$	$2$	$3$	$4$
$P (X = x)$	$\frac{1}{6}$	$\frac{1}{3}$	$\frac{1}{3}$	$\frac{1}{6}$

HARD

Mathematics>Algebra>Probability>Random Variables and its Probability Distributions

If '

X

' has a binomial distribution with parameters

n = 6, p

and

P (X = 2) = 12, P (X = 3) = 5

, then

p =

MEDIUM

Mathematics>Algebra>Probability>Random Variables and its Probability Distributions

Let

x_{i} (1 \leq i \leq 10)

be ten observation of a random variable

X

. If

\sum_{i = 1}^{10} (x_{i} - p) = 3

and

\sum_{i = 1}^{10} {(x_{i} - p)}^{2} = 9

where

0 \neq p \in R

, then the standard deviation of these observations is:

MEDIUM

Mathematics>Algebra>Probability>Random Variables and its Probability Distributions

For the probability distribution given by

$X = x_{i}$	$0$	$1$	$2$
$P_{i}$	$25 / 36$	$5 / 18$	$1 / 36$

The standard deviation $(σ)$ is

MEDIUM

Mathematics>Algebra>Probability>Random Variables and its Probability Distributions

An unbiased coin is tossed

5

times. Suppose that a variable

X

is assigned the value

k

when

k

consecutive heads are obtained for

k = 3, 4, 5,

otherwise

X

takes the value

- 1 .

Then the expected value of

X,

MEDIUM

Mathematics>Algebra>Probability>Random Variables and its Probability Distributions

The probability distribution of a discrete random variable $X$ is given in the following table:

$X = x$	$0$	$1$	$2$
$P (x)$	$4 C^{3}$	$4 C - 13 C^{2}$	$7 C - 1$

; $C > 0$ then $C =$ ________.

HARD

Mathematics>Algebra>Probability>Random Variables and its Probability Distributions

Suppose

A

3 \times 3

matrix consisting of integer entries that are chosen at random from the set

\{- 1000, - 999, \dots 999, 1000\} .

Let

P

be the probability that either

A^{2} = - I

A

is diagonal, where

I

is the

3 \times 3

identity matrix. Then,

MEDIUM

Mathematics>Algebra>Probability>Random Variables and its Probability Distributions

The mean and standard deviation of random variable

X

are

10

and

5

respectively, then

E {(\frac{X - 15}{5})}^{2} =

_________.

MEDIUM

Mathematics>Algebra>Probability>Random Variables and its Probability Distributions

Let $X$ be a random variable with distribution.

$x$	$- 2$	$- 1$	$3$	$4$	$6$
$P (X = x)$	$\frac{1}{5}$	$a$	$\frac{1}{3}$	$\frac{1}{5}$	$b$

If the mean of $X$ is $2.3$ and variance of $X$ is $σ^{2},$ then $100 σ^{2}$ is equal to :

HARD

Mathematics>Algebra>Probability>Random Variables and its Probability Distributions

Let

X

be a random variable such that the probability function of a distribution is given by

P (X = 0) = \frac{1}{2}, P (X = j) = \frac{1}{3^{j}} (j = 1, 2, 3, \dots, \infty) .

Then the mean of the distribution and

P (X

is positive and even

)

respectively, are:

HARD

Mathematics>Algebra>Probability>Random Variables and its Probability Distributions

Let

X

be a random variable which takes values

k

with the probability

k p,

where

k = 1, 2, 3, 4

and

p \in (0, 1),

then the standard deviation of

X

EASY

Mathematics>Algebra>Probability>Random Variables and its Probability Distributions

A random variable

X

has the following probability distribution:

\begin{matrix} \begin{matrix} X : & 1 & \begin{matrix} 2 & 3 & \begin{matrix} 4 & 5 \end{matrix} \end{matrix} \end{matrix} \\ P (X) : \begin{matrix} k^{2} & \begin{matrix} 2 k & k & \begin{matrix} 2 k & 5 k^{2} \end{matrix} \end{matrix} \end{matrix} \end{matrix}

Then,

P (X > 2)

is equal to:

HARD

Mathematics>Algebra>Probability>Random Variables and its Probability Distributions

In a game, a man wins Rs.

100

if he gets

5

6

on a throw of a fair die and loses Rs.

50

for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is :

A player tosses two coins if two heads appears he wins Rs. 4, if one head appears he wins Rs. 2, but if two tails appears he loses Rs. 3. Find the expected sum of money he wins?

Important Questions on Probability

Learn and Prepare for any exam you want !

A player tosses two coins if two heads appears he wins Rs. $4,$ if one head appears he wins Rs. $2$ , but if two tails appears he loses Rs. $3$ . Find the expected sum of money he wins?