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

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An unbiased die is tossed until a number greater than $4$ appears. The probability that an even number of tosses needed, is

50% studentsanswered this correctly

Important Questions on Probability

EASY

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

The mean and variance of a random variable

X

in binomial distribution are

4

and

2

respectively, then

P (X = 1)

HARD

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

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 :

EASY

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

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>Conditional Probability and Multiplication Theorem

A

and

B

are two independent witnesses (i.e., there is no collision between them) in a case. The probability that

A

will speak the truth is

x

and the probability that

B

will speak the truth is

y .

A

and

B

agree in a certain statement. The probability that the statement is true is

EASY

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

Letters in the word

H U L U L U L U

are rearranged. The probability of all three

L

being together is

MEDIUM

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

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>Conditional Probability and Multiplication Theorem

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:

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

EASY

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

A coin is tossed three times. If

X

denotes the absolute difference between the number of heads and the number of tails then

P (X = 1) =

HARD

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

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>Conditional Probability and Multiplication Theorem

A signal which can be green or red with probability

\frac{4}{5}

and

\frac{1}{5}

respectively, is received by station

A

and then transmitted to station

B

. The probability of each station receiving the signal correctly is

\frac{3}{4}

. If the signal received at station

B

is green, then the probability that the original signal is green, is

MEDIUM

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

A box

A

contains

2

white,

3

red and

2

black balls. Another box

B

contains

4

white,

2

red and

3

black balls. If two balls are drawn at random, without replacement from a randomly, selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box

B

is :

HARD

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

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>Conditional Probability and Multiplication Theorem

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>Conditional Probability and Multiplication Theorem

A

and

B

are two events such that

P (A) \neq 0

and

P (B| A) = 1

, then

HARD

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

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>Conditional Probability and Multiplication Theorem

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>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:

EASY

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

A die is thrown four times. The probability of getting perfect square in at least one throw is

EASY

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

If $A$ and $B$ are events such that $P (A) = 0.42, P (B) = 0.48$ and $P (A and B) = 0 .16$ . Then,

$I .$ $P (not A) =0 . 58$

$II .$ $P (not B) = 0.52$

$III .$ $P (A or B) = 0.47$

An unbiased die is tossed until a number greater than 4 appears. The probability that an even number of tosses needed, is

Important Questions on Probability

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An unbiased die is tossed until a number greater than $4$ appears. The probability that an even number of tosses needed, is