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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A fair coin is tossed three times and it is known that at least one head has occurred. Then the probability that at most two heads occur is

50% studentsanswered this correctly

Important Questions on Probability

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Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

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:

MEDIUM

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

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>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>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

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>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) .

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

|X|

denote the number of elements in set

X .

Let

S = \{1, 2, 3, 4, 5, 6\}

be a sample space, where each element is equally likely to occur. If

A

and

B

are independent events associated with

S,

then the number of ordered pairs

(A, B)

such that

1 \leq |B| < |A|,

equals

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

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

HARD

Mathematics>Algebra>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?

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:

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

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

MEDIUM

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

A problem in mathematics is given to three students

A, B, C

and their respective probability of solving the problem is

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

and

\frac{1}{4}

, the probability that the problem will be solved is

MEDIUM

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

Four persons can hit a target correctly with probabilities

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

and

\frac{1}{8}

respectively. If all hit at the target independently, then the probability that the target would be hit, is

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?

EASY

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

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

3

MEDIUM

Mathematics>Algebra>Probability>Conditional Probability and Multiplication Theorem

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>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 :

A fair coin is tossed three times and it is known that at least one head has occurred. Then the probability that at most two heads occur is

Important Questions on Probability

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