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

HARD

Earn 100

A coin is tossed repeatedly. A and B call alternately for winning a prize of Rs. 30 One who calls correctly first wins the prize. A starts the cell. Then the expectation of

50% studentsanswered this correctly

Important Questions on Probability

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Mathematics>Algebra>Probability>Basics of Probability

Four persons independently solve a certain problem correctly with probabilities

\frac{1}{2}, \frac{3}{4}, \frac{1}{4}, \frac{1}{8}

. Then the probability that the problem is solved correctly by at least one of them is

HARD

Mathematics>Algebra>Probability>Basics of Probability

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

MEDIUM

Mathematics>Algebra>Probability>Basics of Probability

For the following distribution function $F (x)$ of a random variable $X$

$x$	$1$	$2$	$3$	$4$	$5$	$6$
$F (x)$	$0.2$	$0.37$	$0.48$	$0.62$	$0.85$	$1$

$P (3 < X \leq 5) =$

HARD

Mathematics>Algebra>Probability>Basics of Probability

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 :

EASY

Mathematics>Algebra>Probability>Basics of Probability

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:

EASY

Mathematics>Algebra>Probability>Basics of Probability

A

and

B

are two events such that

P (A) \neq 0

and

P (B| A) = 1

, then

EASY

Mathematics>Algebra>Probability>Basics of Probability

A random variable

X ∽ B (n, p) .

If values of mean and variance of

X

are

18

and

12

respectively then total number of possible values of

X

are

HARD

Mathematics>Algebra>Probability>Basics of Probability

An experiment succeeds twice as often as it fails. The probability of at least

5

successes in the six trials of this experiment is

HARD

Mathematics>Algebra>Probability>Basics of Probability

If the mean and the variance of a binomial variate

X

are

2 & 1

respectively, then the probability that

X

takes a value greater than or equal to one is:

MEDIUM

Mathematics>Algebra>Probability>Basics of Probability

If a fair coin is tossed

5

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

HARD

Mathematics>Algebra>Probability>Basics of Probability

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>Basics of Probability

An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered

1, 2, 3, \dots, 9

is randomly picked and the number on the card is noted. The probability that the noted number is either

7

8

MEDIUM

Mathematics>Algebra>Probability>Basics of Probability

A bag contains

4

red and

6

black balls. A ball is drawn at random from the bag, its color is observed and this ball along with two additional balls of the same color are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is:

EASY

Mathematics>Algebra>Probability>Basics of Probability

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>Basics of Probability

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

HARD

Mathematics>Algebra>Probability>Basics of Probability

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

. One of the two boxes, box

I

and box

II

, was selected at random and a ball was drawn randomly out of this box. The ball was found to be red. If the probability that this red ball was drawn from box

II

\frac{1}{3}

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

n_{1}, n_{2}, n_{3} & n_{4}

is(are)

HARD

Mathematics>Algebra>Probability>Basics of Probability

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)

EASY

Mathematics>Algebra>Probability>Basics of Probability

A

and

B

are events with

P (A \cup B) = \frac{3}{4}, P (A^{'}) = \frac{2}{3}

and

P (A \cap B) = \frac{1}{4}

then

P (B)

HARD

Mathematics>Algebra>Probability>Basics of Probability

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 :

HARD

Mathematics>Algebra>Probability>Basics of Probability

A computer producing factory has only two plants $T_{1}$ and $T_{2}$ . Plant $T_{1}$ produces $20 %$ and plant $T_{2}$ produces $80 %$ of the total computers produced. $7 %$ of computers produced in the factory turn out to be defective. The probability that a computer turns out to be defective which is produced in plant $T_{1}$ is ten times of the computers produced in the plant $T_{2}$ . A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant $T_{2}$ is

A coin is tossed repeatedly. A and B call alternately for winning a prize of Rs. 30 One who calls correctly first wins the prize. A starts the cell. Then the expectation of

Important Questions on Probability

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