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In a lottery, there are 10 prize and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?

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Important Questions on Probability

MEDIUM

Mathematics>Algebra>Probability>Axiomatic Approach to 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.

HARD

Mathematics>Algebra>Probability>Axiomatic Approach to 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>Algebra>Probability>Axiomatic Approach to 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>Algebra>Probability>Axiomatic Approach to Probability

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

EASY

Mathematics>Algebra>Probability>Axiomatic Approach to Probability

What is the probability that a number selected from numbers

1, 2, 3,_______30

, is a prime number, when each of the given numbers is equally likely to be selected?

HARD

Mathematics>Algebra>Probability>Axiomatic Approach to 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:

EASY

Mathematics>Algebra>Probability>Axiomatic Approach to 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)

MEDIUM

Mathematics>Algebra>Probability>Axiomatic Approach to 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:

MEDIUM

Mathematics>Algebra>Probability>Axiomatic Approach to Probability

There are

6

red balls and

4

yellow balls in a bag. Two balls are simultaneously drawn at random. What is the probability that both the balls are of same colour?

MEDIUM

Mathematics>Algebra>Probability>Axiomatic Approach to 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:

HARD

Mathematics>Algebra>Probability>Axiomatic Approach to 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>Axiomatic Approach to Probability

There are

3

red balls,

4

blue balls and

5

white balls.

2

balls are chosen randomly. Find the probability that one is red and the other is white.

HARD

Mathematics>Algebra>Probability>Axiomatic Approach to 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:

HARD

Mathematics>Algebra>Probability>Axiomatic Approach to 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

EASY

Mathematics>Algebra>Probability>Axiomatic Approach to Probability

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

5

MEDIUM

Mathematics>Algebra>Probability>Axiomatic Approach to 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>Algebra>Probability>Axiomatic Approach to 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>Algebra>Probability>Axiomatic Approach to 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>Algebra>Probability>Axiomatic Approach to Probability

A bag contains

6

black and

8

white balls. One ball is drawn at random. What is the probability that the ball drawn is white?

MEDIUM

Mathematics>Algebra>Probability>Axiomatic Approach to Probability

A bag contains

3

red balls,

5

yellow balls and

7

pink balls. If one ball is drawn at random from the bag, what is the probability that it is either pink or red?

In a lottery, there are 10 prize and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?

Important Questions on Probability

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