Let A and E be any two events with positive probabilities Statement I: P E / A ≥ P A / E P E . Statement II: P A / E ≥ P A ∩ E .

Statement - I is false, Statement - II is true

Statement - I is true, Statement - II is false

Let A and B be two events such that P A ∪ B ¯ = 1 6 , P A ∩ B = 1 4 and P A ¯ = 1 4 , where A ¯ stands for the complement of the event A . Then the events A and B are

Independent but not equally likely.

Independent and equally likely.

Mutually exclusive and independent.

Equally likely but not independent.

Let E 1 and E 2 be two events such that the conditional probabilities P E 1 ∣ E 2 = 1 2 , P E 2 ∣ E 1 = 3 4 and P E 1 ∩ E 2 = 1 8 . Then

P E 1 ∩ E 2 ' = P E 1 · P E 2

P E 1 ' ∩ E 2 ' = P E 1 ' · P E 2

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

HARD

JEE Main

IMPORTANT

Earn 100

Let $A$ and $E$ be any two events with positive probabilities

Statement I: $P (E / A) \geq P (A / E) P (E) .$

Statement II: $P (A / E) \geq P (A \cap E) .$

50% studentsanswered this correctly

Important Questions on Probability

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 9th April 2014>Q 84

A

and

B

are two events such that

P (A \cup B) = P (A \cap B)

, then the incorrect statement amongst the following statements is :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 6th April 2014>Q 85

Let

A

and

B

be two events such that

P (\bar{A \cup B}) = \frac{1}{6}, P (A \cap B) = \frac{1}{4}

and

P (\bar{A}) = \frac{1}{4},

where

\bar{A}

stands for the complement of the event

A

. Then the events

A

and

B

are

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 7th April 2013>Q 86

A multiple choice examination has

5

questions. Each question has three alternative answers out of which exactly one is correct. The probability that a student will get

4

or more correct answers just by guessing is :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 24 June 2022 Shift 1>Q 87

Bag

A

contains

2

white,

1

black and

3

red balls and bag

B

contains

3

black,

2

red and

n

white balls. One bag is chosen at random and

2

balls drawn from it at random are found to be

1

red and

1

black. If the probability that both balls come from Bag

A

\frac{6}{11}

, then

n

is equal to _____

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 24 June 2022 Shift 1>Q 88

If a random variable

X

follows the Binomial distribution

B (33, p)

such that

3 P (X = 0) = P (X = 1)

, then the value of

\frac{P (X = 15)}{P (X = 18)} - \frac{P (X = 16)}{P (X = 17)}

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 24 June 2022 Shift 2>Q 89

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

$X$	$0$	$1$	$2$	$3$	$4$
$P (X)$	$k$	$2 k$	$4 k$	$6 k$	$8 k$

The value of $P (\frac{1 < x < 4}{x \leq 2})$ is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 24 June 2022 Shift 2>Q 90

In an examination, there are

10

true-false type questions. Out of

10

, a student can guess the answer of

4

questions correctly with probability

\frac{3}{4}

and the remaining

6

questions correctly with probability

\frac{1}{4}

. If the probability that the student guesses the answers of exactly

8

questions correctly out of

10

\frac{27 k}{4^{10}}

, then

k

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 25 June 2022 Shift 1>Q 91

Let

E_{1}

and

E_{2}

be two events such that the conditional probabilities

P (E_{1} ∣ E_{2}) = \frac{1}{2}

P (E_{2} ∣ E_{1}) = \frac{3}{4}

and

P (E_{1} \cap E_{2}) = \frac{1}{8}

. Then

Let A and E be any two events with positive probabilities Statement I: PE/A≥PA/EPE. Statement II: PA/E≥PA∩E.

Important Questions on Probability

Learn and Prepare for any exam you want !

Let $A$ and $E$ be any two events with positive probabilities

Statement I: $P (E / A) \geq P (A / E) P (E) .$

Statement II: $P (A / E) \geq P (A \cap E) .$