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

When a missile is fired from a ship, the probability that it is intercepted is $\frac{1}{3}$ and the probability that the missile hits the target, given that it is not intercepted, is $\frac{3}{4} .$ If three missiles are fired independently from the ship, then the probability that all three hit the target, is:

36.36% studentsanswered this correctly

Important Questions on Probability

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 25 Feb 2021 Shift 2>Q 28

Let

A

be a set of all

4

-digit natural numbers whose exactly one digit is

7

. Then the probability that a randomly chosen element of

A

leaves remainder

2

when divided by

5

is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 25 Feb 2021 Shift 2>Q 29

In a group of

400

people,

160

are smokers and non-vegetarian;

100

are smokers and vegetarian and the remaining

140

are non-smokers and vegetarian. Their chances of getting a particular chest disorder are

35 %, 20 %

and

10 %

respectively. A person is chosen from the group at random and is found to be suffering from the chest disorder. The probability that the selected person is a smoker and non-vegetarian is :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 26 Feb 2021 Shift 1>Q 30

A fair coin is tossed a fixed number of times. If the probability of getting

7

heads is equal to probability of getting

9

heads, then the probability of getting

2

heads is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 26 Feb 2021 Shift 2>Q 31

A seven digit number is formed using digits

3, 3, 4, 4, 4, 5, 5

. The probability, that number so formed is divisible by

2

, is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 2 September 2020 Shift 1>Q 32

Box

1

contains

30

cards numbered

1

30

and Box

2

contains

20

cards numbered

31

50

. A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box

1

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 2 September 2020 Shift 2>Q 33

Let

E^{C}

denote the complement of an event

E

. Let

E_{1}, E_{2}

and

E_{3}

be any pairwise independent events with

P (E_{1}) > 0

and

P (E_{1} \cap E_{2} \cap E_{3}) = 0

, then

P ((E_{2}^{C} \cap E_{3}^{C}) / E_{1})

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 3 September 2020 Shift 1>Q 34

A die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of

4

. Then the conditional probability that the score

4

has appeared at least once is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 3 September 2020 Shift 2>Q 35

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:

When a missile is fired from a ship, the probability that it is intercepted is 13 and the probability that the missile hits the target, given that it is not intercepted, is 34. If three missiles are fired independently from the ship, then the probability that all three hit the target, is:

Important Questions on Probability

Learn and Prepare for any exam you want !