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.

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Two dice are tossed. Let $A$ be the event that the first die shows an even number and $B$ be the event that the second die shows an odd number. The two event $A$ and $B$ are

50% studentsanswered this correctly

Important Questions on Probability

EASY

Mathematics>Algebra>Probability>Events

For the events

A

and

B,

P (A) = \frac{3}{4}, P (B) = \frac{1}{5}, P (A \cap B) = \frac{1}{20}

then

P (\frac{A}{B}) =

HARD

Mathematics>Algebra>Probability>Events

In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to :

MEDIUM

Mathematics>Algebra>Probability>Events

If a fair coin is tossed

5

times, the probability that heads does not occur two or more times in a row is

EASY

Mathematics>Algebra>Probability>Events

A coin is tossed and a die is rolled. The probability that the coin shows head and the die shows

3

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Mathematics>Algebra>Probability>Events

Six persons $A, B, C, X, Y & Z$ go for an interview. What is the probability of selection of $A$ and $Y$ in the interview?

EASY

Mathematics>Algebra>Probability>Events

The probability that a person will develop immunity after vaccination is

0.8.

8

people are given the vaccine then probability that all develop immunity is equal to

EASY

Mathematics>Algebra>Probability>Events

An urn contains

5

red and

2

green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is:

HARD

Mathematics>Algebra>Probability>Events

Let

E & F

be two independent events. The probability that

E & F

happen is

\frac{1}{12}

and the probability that neither

E

nor

F

happens is

\frac{1}{2}

, then a value of

\frac{P (E)}{P (F)}

is:

EASY

Mathematics>Algebra>Probability>Events

In a college, $\frac{1}{5} t h$ of the girls and $\frac{1}{8} th$ of the boys took part in a social camp. The total number of students in the college took part in the camp is:

HARD

Mathematics>Algebra>Probability>Events

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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Mathematics>Algebra>Probability>Events

In a class,

40

% of students study Maths and Science and

60

% of students study Maths. What is the probability of a students studying Science given the student is already studying Maths?

EASY

Mathematics>Algebra>Probability>Events

Let

A

and

B

are two mutually exclusive events with

P (A) = \frac{1}{3}

and

P (B) = \frac{1}{4} .

What is the value

P (\bar{A} \cap \bar{B}) ?

EASY

Mathematics>Algebra>Probability>Events

A

and

B

are any two events such that

P (A) + P (B) - P (A a n d B) = P (A)

, then

HARD

Mathematics>Algebra>Probability>Events

Let

A, B

and

C

be three events, which are pair-wise independent and

\bar{E}

denotes the complement of an event

E

. If

P (A \cap B \cap C) = 0

and

P (C) > 0,

then

P [(\bar{A} \cap \bar{B}) | C]

is equal to

EASY

Mathematics>Algebra>Probability>Events

A

and

B

are two events such that

P (A) \neq 0

and

P (B| A) = 1

, then

HARD

Mathematics>Algebra>Probability>Events

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) .

HARD

Mathematics>Algebra>Probability>Events

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

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Mathematics>Algebra>Probability>Events

Two persons

A

and

B

throw a die alternatively till one of them gets a three and wins the game. Find their respective probabilities of winning.

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Mathematics>Algebra>Probability>Events

A determinant of second order is made with the elements 0, 1. What is the probability that the determinant is positive?

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Mathematics>Algebra>Probability>Events

A person throws two fair dice. He wins Rs.

15

for throwing a doublet (same numbers on the two dice), wins Rs

12

when the throw results in the sum of

9

, and loses Rs.

6

for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is:

Two dice are tossed. Let A be the event that the first die shows an even number and B be the event that the second die shows an odd number. The two event A and B are

Important Questions on Probability

Learn and Prepare for any exam you want !

Two dice are tossed. Let $A$ be the event that the first die shows an even number and $B$ be the event that the second die shows an odd number. The two event $A$ and $B$ are