Two dice are thrown independently. Let A be the event that the number appeared on the 1 st die is less than the number appeared on the 2 nd die, B be the event that the number appeared on the 1 st die is even and that on the second die is odd, and C be the event that the number appeared on the 1 st die is odd and that on the 2 nd is even. Then

The number of favourable cases of the event ( A ∪ B ) ∩ C is 6

The number of favourable cases of the events A , B and C are 15 , 6 and 6 respectively

MEDIUM

JEE Main

IMPORTANT

Earn 100

Let $S = {1, 2, 3, 4, 5, 6} .$ Then the probability that a randomly chosen onto function $g$ from $S$ to $S$ satisfies $g (3) = 2 g (1)$ is :

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Important Questions on Probability

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 1 September 2021 Shift 2>Q 7

Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is :

Question Image

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 1 September 2021 Shift 2>Q 8

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 :

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 20 July 2021 Shift 1>Q 9

Words with or without meaning are to be formed using all the letters of the word

EXAMINATION

. The probability that the letter

M

appears at the fourth position in any such word is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 20 July 2021 Shift 1>Q 10

The probability of selecting integers

a \in [- 5, 30]

such that

x^{2} + 2 (a + 4) x - 5 a + 64 > 0

, for all

x \in R

, is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 20 July 2021 Shift 2>Q 11

Let

A, B

and

C

be three events such that the probability that exactly one of

A

and

B

occurs is

(1 - k),

the probability that exactly one of

B

and

C

occurs is

(1 - 2 k),

the probability that exactly one of

C

and

A

occurs is

(1 - k)

and the probability of all

A, B

and

C

occur simultaneously is

k^{2},

where

0 < k < 1 .

Then the probability that at least one of

A, B

and

C

occur is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 22 July 2021 Shift 1>Q 12

Four dice are thrown simultaneously and the numbers shown on these dice are recorded in

2 \times 2

matrices. The probability that such formed matrices have all different entries and are non-singular, is:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 25 July 2021 Shift 1>Q 13

Let

9

distinct balls be distributed among

4

boxes,

B_{1}, B_{2}, B_{3}

and

B_{4}

. If the probability that

B_{3}

contains exactly

3

balls is

k {(\frac{3}{4})}^{9}

then

k

lies in the set :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 25 July 2021 Shift 2>Q 14

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:

Let S={1, 2, 3, 4, 5, 6}. Then the probability that a randomly chosen onto function g from S to S satisfies g3=2 g1 is :

Important Questions on Probability

Learn and Prepare for any exam you want !

Let $S = {1, 2, 3, 4, 5, 6} .$ Then the probability that a randomly chosen onto function $g$ from $S$ to $S$ satisfies $g (3) = 2 g (1)$ is :