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Two fair dice are rolled simultaneously. It is found that one of them shows odd prime number. The probability that remaining die also shows an odd prime number, is

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Important Questions on Probability

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Mathematics>Algebra>Probability>Axiomatic Approach to Probability

A quadratic equation

a x^{2} + b x + c = 0

with distinct coefficients is formed. It

a, b, c

are chosen from the numbers

2, 3

and

5,

then the probability that the equation has real roots is

EASY

Mathematics>Algebra>Probability>Axiomatic Approach to Probability

The probability that among

7

persons, no

2

were born on the same day of a week is

HARD

Mathematics>Algebra>Probability>Axiomatic Approach to Probability

If two different numbers are taken from the set

\{0, 1, 2, 3, . . . . ., 10\}

; then the probability that their sum as well as absolute difference are both multiple of

4

, is:

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Mathematics>Algebra>Probability>Axiomatic Approach to Probability

A letter is taken at random from the word "STATISTICS" and another letter is taken at random from the word "ASSISTANT". The probability that they are same letters is

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Mathematics>Algebra>Probability>Axiomatic Approach to Probability

Directions: Each of the following sentences in this section has a blank space and four words or group of words given after the sentence. Select the word or group of words you consider most appropriate for the blank space and indicate your response on the Answer Sheet accordingly.

Every rash driver becomes a ____ killer.

EASY

Mathematics>Algebra>Probability>Axiomatic Approach to Probability

An ellipse of eccentricity

\frac{2 \sqrt{2}}{3}

is inscribed in a circle. A point is chosen inside the circle at random. The probability that the point lies outside the ellipse is

HARD

Mathematics>Algebra>Probability>Axiomatic Approach to Probability

Two different families

A

and

B

are blessed with equal number of children. There are

3

tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family

B

\frac{1}{12},

then the number of children in each family is

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Mathematics>Algebra>Probability>Axiomatic Approach to Probability

A box contains coupons labelled

1, 2, . . . ., 100

. Five coupons are picked at random one after another without replacement. Let the numbers on the coupons be

x_{1}, x_{2}, \dots ., x_{5}

. What is the probability that

x_{1} > x_{2} > x_{3} a n d x_{3} < x_{4} < x_{5}

HARD

Mathematics>Algebra>Probability>Axiomatic Approach to Probability

A multiple choice examination has

5

questions. Each question has three alternative answers out of which exactly one is correct. The probability that a student will get

4

or more correct answers just by guessing is :

HARD

Mathematics>Algebra>Probability>Axiomatic Approach to Probability

If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is:

HARD

Mathematics>Algebra>Probability>Axiomatic Approach to Probability

If a

3 -

digit number is randomly chosen. What is the probability that either the number itself or some permutation of the number (which is a

3 -

digit number) is divisible by

4

and

5 ?

EASY

Mathematics>Algebra>Probability>Axiomatic Approach to Probability

Two sentences are given below and you are required to find the correct sentence which combines both the sentences.

Which is the correct combination of the given two sentences?

He is too tired. He could not stand.

HARD

Mathematics>Algebra>Probability>Axiomatic Approach to Probability

From a group of

10

men and

5

women, four member committees are to be formed each of which must contain at least one women. Then the probability for these committees to have more women than men, is :

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Mathematics>Algebra>Probability>Axiomatic Approach to Probability

In the following sentence, a blank space with four options is given. Select whichever preposition or determiner you consider the most appropriate for the blank space.

These are the good rules to live _____.

HARD

Mathematics>Algebra>Probability>Axiomatic Approach to Probability

A box contains coupons labeled 1, 2, 3 .....

n

. A coupon is picked at random and the number

x

is noted. The coupon is put back into the box and a new coupon is picked at random. The number is

y

. Then the probability that one of the numbers

x, y

divides the other is (in the options below

[r]

denotes the largest integer less than or equal to

r

)

HARD

Mathematics>Algebra>Probability>Axiomatic Approach to Probability

An urn contains marbles of four colours : red, white, blue and green. When four marbles are drawn without replacement, the following events are equally likely:

(i) The selection of four red marbles

(ii) The selection of one white and three red marbles

(iii) The selection of one white, one blue and two red marbles

(iv) The selection of one marble of each colour

The smallest total number of marbles satisfying the given condition is

HARD

Mathematics>Algebra>Probability>Axiomatic Approach to Probability

Let

X_{n} = \{1, 2, 3, \dots ., n\}

and let a subset

A

X_{n}

be chosen so that every pair of elements of A differ by at least

3

. (For example, if

n = 5,

A can be

\emptyset, \{2\} o r \{1, 5\}

Among others). When

n = 10,

let the probability that

1 \in A

p

and let the probability that

2 \in A

q .

Then-

HARD

Mathematics>Algebra>Probability>Axiomatic Approach to Probability

Let

X

be a set containing

10

elements and

P (X)

be its power set. If

A

and

B

are picked up at random from

P (X)

, with replacement, then the probability that

A

and

B

have equal number of elements is:

HARD

Mathematics>Algebra>Probability>Axiomatic Approach to Probability

If $12$ identical balls are to be placed in $3$ identical boxes, then the probability that one of the boxes contains exactly $3$ balls is

EASY

Mathematics>Algebra>Probability>Axiomatic Approach to Probability

Letters in the word

H U L U L U L U

are rearranged. The probability of all three

L

being together is

Two fair dice are rolled simultaneously. It is found that one of them shows odd prime number. The probability that remaining die also shows an odd prime number, is

Important Questions on Probability

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