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 complement of event A . Then events A and B are

independent but not equally likely.

mutually exclusive and independent.

equally likely but not independent.

equally likely and mutually exclusive.

EASY

Earn 100

Two students come late to the class and give reasons why they are late. The probability that the teacher believes the excuse of each student is $0.4 .$ Let $p$ be the probability that the teacher believes both the students and $q$ be the probability that the teacher believes the second student but not the first. Then

50% studentsanswered this correctly

Important Questions on Probability

EASY

Mathematics>Statistics and Probability>Probability>Algebra of Probability

Let

A

and

B

be two events such that the probability that exactly one of them occurs is

\frac{2}{5}

and the probability that

A

B

occurs is

\frac{1}{2}

, then the probability of both of them occur together is

HARD

Mathematics>Statistics and Probability>Probability>Algebra of Probability

Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than

99 %

is:

MEDIUM

Mathematics>Statistics and Probability>Probability>Algebra of Probability

In a box, there are

20

cards, out of which

10

are labelled as

A

and the remaining

10

are labelled as

B

. Cards are drawn at random, one after the other and with replacement, till a second

A

card is obtained. The probability that the second

A

card appears before the third

B

card is:

EASY

Mathematics>Statistics and Probability>Probability>Algebra 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>Statistics and Probability>Probability>Algebra 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

MEDIUM

Mathematics>Statistics and Probability>Probability>Algebra of Probability

The probabilities of three events

A, B

and

C

are given

P (A) = 0.6, P (B) = 0.4

and

P (C) = 0.5

. If

P (A \cup B) = 0.8, P (A \cap C) = 0.3, P (A \cap B \cap C) = 0.2, P (B \cap C) = β

and

P (A \cup B \cup C) = α

, where

0.85 \leq α \leq 0.95,

then

β

lies in the interval :

EASY

Mathematics>Statistics and Probability>Probability>Algebra of Probability

If three dices are thrown then the probability that the sum of the numbers on their uppermost faces to be atleast

5

EASY

Mathematics>Statistics and Probability>Probability>Algebra of Probability

Let

A

and

B

are two independent events. If the probability that both

A

and

B

occur together is

\frac{1}{6}

and the probability that neither of them occurs is

\frac{1}{3}

, then the probability of occurrence of

A

HARD

Mathematics>Statistics and Probability>Probability>Algebra of Probability

Three persons P, Q and R independently try to hit a target. If the probabilities of their hitting the target are

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

and

\frac{5}{8}

respectively, then the probability that the target is hit by P or Q but not by R is:

HARD

Mathematics>Statistics and Probability>Probability>Algebra of Probability

An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is:

HARD

Mathematics>Statistics and Probability>Probability>Algebra of Probability

Consider the following events:

$E_{1} :$ Six fair dice are rolled and at least one die shows six
$E_{2} :$ Twelve fair dice are rolled and at least two dice show six
Let $p_{1}$ be the probability of $E_{1}$ and $p_{2}$ be the probability of $E_{2} .$ Which of the following is true ?

HARD

Mathematics>Statistics and Probability>Probability>Algebra of Probability

For three events,

A, B

and

C,

P

(Exactly one of

A

B

occurs)

= P

(Exactly one of

B

C

occurs)

= P

(Exactly one of

C

A

occurs)

= \frac{1}{4}

and

P

(All the three events occur simultaneously)

= \frac{1}{16} .

Then the probability that at least one of the events occurs, is:

HARD

Mathematics>Statistics and Probability>Probability>Algebra of Probability

In a class of

60

students,

40

opted for NCC,

30

opted for NSS and

20

opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is :

EASY

Mathematics>Statistics and Probability>Probability>Algebra of Probability

Let the probability distribution of a random variable $X$ be given by

$X$	$- 1$	$0$	$1$	$2$	$3$
$p (X)$	$a$	$2 a$	$3 a$	$4 a$	$5 a$

Then the expectation of $X$ is

HARD

Mathematics>Statistics and Probability>Probability>Algebra of Probability

Let

A

and

B

be two events such that

P (A \cup B) = \frac{1}{6}, P (A \cap B) = \frac{1}{4}

, and

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

, where

\bar{A}

stands for complement of event

A

. Then events

A

and

B

are

MEDIUM

Mathematics>Statistics and Probability>Probability>Algebra of Probability

An executive in a company makes on an average

5

telephone calls per hour at a cost of Rs.

2

per call. The probability that in any hour the cost of the calls exceeds a sum of Rs.

4

MEDIUM

Mathematics>Statistics and Probability>Probability>Algebra of Probability

The probability that atleast one of the events

A

and

B

occur is

0.6 .

A

and

B

occur simultaneously with probability

0.2

, then

P (\bar{A}) + P (\bar{B})

HARD

Mathematics>Statistics and Probability>Probability>Algebra 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 :

MEDIUM

Mathematics>Statistics and Probability>Probability>Algebra of Probability

Three players

A, B

and

C

play a game. The probability that

A, B

and

C

will finish the game are respectively

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

and

\frac{1}{4}

.

The probability that the game is finished is.

MEDIUM

Mathematics>Statistics and Probability>Probability>Algebra of Probability

If the probability of hitting a target by a shooter, in any shot is

\frac{1}{3},

then the minimum number of independent shots at the target required by him so that the probability of hitting the target at least once is greater than

\frac{5}{6},

is:

Important Questions on Probability

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