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

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A six faced die is biased such that $3 \times P$ (a prime number) $= 6 \times P$ (a composite number) $= 2 \times P (1)$ . Let $X$ be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of $X$ 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 - 28 July 2022 Shift 1>Q 112

Out of

60 %

female and

40 %

male candidates appearing in an exam,

60 %

candidates qualify it. The number of females qualifying the exam is twice the number of males qualifying it. A candidate is randomly chosen from the qualified candidates. The probability, that the chosen candidate is a female, is

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JEE Main

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 28 July 2022 Shift 2>Q 113

Let $A$ and $B$ be two events such that $P (B ∣ A) = \frac{2}{5}$ , $P (A ∣ B) = \frac{1}{7}$ and $P (A \cap B) = \frac{1}{9}$ . Consider

$(S 1) : P (A^{'} \cup B) = \frac{5}{6}$ ,

$(S 2) : P (A^{'} \cap B^{'}) = \frac{1}{18}$ . Then

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 28 July 2022 Shift 2>Q 114

A bag contains

4

white and

6

black balls. Three balls are drawn at random from the bag. Let

X

be the number of white balls, among the drawn balls. If

σ^{2}

is the variance of

X

, then

100 σ^{2}

is equal to

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 29 July 2022 Shift 1>Q 115

Let

S = \{1, 2, 3, \dots, 2022\}

. Then the probability, that a randomly chosen number

n

from the set

S

such that

H C F (n, 2022) = 1

, is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 29 July 2022 Shift 2>Q 116

Bag

I

contains

3

red,

4

black and

3

white balls and Bag

II

contains

2

red,

5

black and

2

white balls. One ball is transferred from Bag

I

to Bag

II

and then a ball is draw from Bag

II

. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 29 July 2022 Shift 2>Q 117

The sum and product of the mean and variance of a binomial distribution are

82.5

and

1350

respectively. They the number of trials in the binomial distribution is

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 24 January 2023 Shift 1>Q 118

Let $Ω$ be the sample space and $A \subseteq Ω$ be an event. Given below are two statements:

$(S_{1})$ : If $P (A) = 0$ , then $A = ϕ$

$(S_{2})$ : If $P (A) = 1$ , then $A = Ω$

Then

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 24 January 2023 Shift 2>Q 119

The urns

A, B

and

C

contains

4

red,

6

black;

5

red,

5

black and

λ

red,

4

black balls respectively. One of the urns is selected at random and a ball is drawn. If the ball drawn is red and the probability that it is drawn from urn

C

0.4

, then the square of length of the side of largest equilateral triangle, inscribed in the parabola

y^{2} = λ x

with one vertex at vertex of parabola is

A six faced die is biased such that 3×P(a prime number)=6×P(a composite number)=2×P1. Let X be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of X is

Important Questions on Probability

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A six faced die is biased such that $3 \times P$ (a prime number) $= 6 \times P$ (a composite number) $= 2 \times P (1)$ . Let $X$ be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of $X$ is