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Two dice are thrown and the sum of the numbers appearing on the dice is observed to be a multiple of $4$ . If $p$ is the conditional probability that number $4$ has appeared atleast once, then $3 p + 2 =$

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Important Questions on Probability

EASY

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

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:

MEDIUM

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

Assume that each born child is equally likely to be a boy or girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is:

HARD

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

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

HARD

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

A bag contains

6

red balls and

10

green balls.

3

balls are drawn from it one by one randomly without replacement. If the

3^{rd}

drawn ball is red, then the probability that the first two drawn balls are green is

HARD

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

Let

n_{1} & n_{2}

be the number of red and black balls, respectively, in box

I

. Let

n_{3} & n_{4}

be the number of red and black balls, respectively, in box

II

. A ball is drawn at random from box

I

and transferred to box

II

. If the probability of drawing a red ball from box

I

, after this transfer, is

\frac{1}{3}

, then the correct options(s) with the possible values of

n_{1} & n_{2}

is(are)

MEDIUM

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

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

EASY

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

A

and

B

are two events of a sample space

S

such that

P (A) = 0.2, P (B) = 0.6

and

P (A | B) = 0.5,

then

P (A^{'} | B) =

EASY

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

Two dice

A

and

B

are rolled. If it is known that the number on

B

5,

then the probability that the sum of the numbers on the two dice will be greater than

9

HARD

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

A

and

B

are any two events such that

P (A) = \frac{2}{5}

and

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

then the conditional probability,

P (A| (A^{'} \cup B^{'})),

where

A^{'}

denotes the complement of

A

, is equal to :

HARD

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

Let

X

and

Y

be two events such that

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

P (X| Y) = \frac{1}{2}

and

P (Y | X) = \frac{2}{5} .

Then

EASY

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

It is given that the events

A

and

B

are such that

P (A) = \frac{1}{4}, P (A ∣ B) = \frac{1}{2}

and

P (B ∣ A) = \frac{2}{3}

. Then

P (B)

EASY

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

A

and

B

are any two events such that

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

, then

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Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

Three numbers are chosen at random without replacement from

{1, 2, 3, \dots \dots, 8}

. The probability that their minimum is

3

, given that their maximum is

6

, is

EASY

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

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}) =

EASY

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

Two numbers are selected at random from the set

\{1, 2, 3, \dots \dots, 13\} .

If the sum of the selected numbers is even, the probability that both the numbers are odd is

MEDIUM

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

Two cards are drawn from a pack of well shuffled

52

playing cards one by one without replacement. Then the probability that both cards are queens is

EASY

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

A

and

B

are two events such that

P (A) = \frac{1}{3}, P (B) = \frac{1}{2}

and

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

then

P (A / B)

MEDIUM

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

Let

A

and

B

be two non-null events such that

A \subset B .

Then, which of the following statements is always correct?

HARD

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

One ticket is selected at random from

50

tickets numbered

00, 01, 02, . . . ., 49

. Then, the probability that the sum of the digits on the selected ticket is

8

, given that the product of these digits is zero, equals

EASY

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

A

and

B

are two events such that

P (A) \neq 0

and

P (B| A) = 1

, then

Two dice are thrown and the sum of the numbers appearing on the dice is observed to be a multiple of 4. If p is the conditional probability that number 4 has appeared atleast once, then 3p+2=

Important Questions on Probability

Learn and Prepare for any exam you want !

Two dice are thrown and the sum of the numbers appearing on the dice is observed to be a multiple of $4$ . If $p$ is the conditional probability that number $4$ has appeared atleast once, then $3 p + 2 =$