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

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Earn 100

If $A & B$ are events such that $P (A \cup B) = \frac{5}{6}, P (\bar{A}) = \frac{1}{4}, P (B) = \frac{1}{3},$ then $A$ and $B$ are

50% studentsanswered this correctly

Important Questions on Probability

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Mathematics>Statistics and Probability>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 :

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Mathematics>Statistics and Probability>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

EASY

Mathematics>Statistics and Probability>Probability>Conditional Probability and Multiplication Theorem

A

and

B

are two events such that

P (A) \neq 0

and

P (B| A) = 1

, then

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Mathematics>Statistics and Probability>Probability>Conditional Probability and Multiplication Theorem

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

5

successes in the six trials of this experiment is

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Mathematics>Statistics and Probability>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:

MEDIUM

Mathematics>Statistics and Probability>Probability>Conditional Probability and Multiplication Theorem

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>Statistics and Probability>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

HARD

Mathematics>Statistics and Probability>Probability>Conditional Probability and Multiplication Theorem

The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least

90 %

is:

EASY

Mathematics>Statistics and Probability>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)

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Mathematics>Statistics and Probability>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

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Mathematics>Statistics and Probability>Probability>Conditional Probability and Multiplication Theorem

Let two fair six-faced dice

A

and

B

be thrown simultaneously. If

E_{1}

is the event that die

A

shows up four,

E_{2}

is the event that die

B

shows up two and

E_{3}

is the event that the sum of numbers on both dice is odd, then which of the following statements is not true?

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Mathematics>Statistics and Probability>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 :

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Mathematics>Statistics and Probability>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 :

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Mathematics>Statistics and Probability>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) .

MEDIUM

Mathematics>Statistics and Probability>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?

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Mathematics>Statistics and Probability>Probability>Conditional Probability and Multiplication Theorem

For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is

\frac{4}{5},

then the probability that he is unable to solve less than two problems is

MEDIUM

Mathematics>Statistics and Probability>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:

MEDIUM

Mathematics>Statistics and Probability>Probability>Conditional Probability and Multiplication Theorem

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

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

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

EASY

Mathematics>Statistics and Probability>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:

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Mathematics>Statistics and Probability>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

If A & B are events such that P A∪B=56 , P A-=14 , PB=13 , then A and B are

Important Questions on Probability

Learn and Prepare for any exam you want !

If $A & B$ are events such that $P (A \cup B) = \frac{5}{6}, P (\bar{A}) = \frac{1}{4}, P (B) = \frac{1}{3},$ then $A$ and $B$ are