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If any four numbers are selected and they are multiplied, then the probability that the last digit will 1,3,5 or 7, is

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Important Questions on Probability

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Mathematics>Algebra>Probability>Basics of 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>Basics of 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

HARD

Mathematics>Algebra>Probability>Basics of 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>Basics of 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>Basics of Probability

Six persons $A, B, C, X, Y & Z$ go for an interview. What is the probability of selection of $A$ and $Y$ in the interview?

HARD

Mathematics>Algebra>Probability>Basics of 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

HARD

Mathematics>Algebra>Probability>Basics of 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 :

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Mathematics>Algebra>Probability>Basics of 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

EASY

Mathematics>Algebra>Probability>Basics of Probability

In a college, $\frac{1}{5} t h$ of the girls and $\frac{1}{8} th$ of the boys took part in a social camp. The total number of students in the college took part in the camp is:

HARD

Mathematics>Algebra>Probability>Basics of Probability

Four dice are thrown simultaneously and the numbers shown on these dice are recorded in

2 \times 2

matrices. The probability that such formed matrices have all different entries and are non-singular, is:

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Mathematics>Algebra>Probability>Basics of 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

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Mathematics>Algebra>Probability>Basics of Probability

A determinant of second order is made with the elements 0, 1. What is the probability that the determinant is positive?

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Mathematics>Algebra>Probability>Basics of 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

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Mathematics>Algebra>Probability>Basics of Probability

The probability that among

7

persons, no

2

were born on the same day of a week is

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Mathematics>Algebra>Probability>Basics of Probability

Let

a

and

b

2

consecutive integers selected from the first

20

natural numbers. The probability that

\sqrt{a^{2} + b^{2} + a^{2} b^{2}}

is an odd positive integer is

HARD

Mathematics>Algebra>Probability>Basics of 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 :

HARD

Mathematics>Algebra>Probability>Basics of 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 ?

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Mathematics>Algebra>Probability>Basics of Probability

Two persons

A

and

B

throw a die alternatively till one of them gets a three and wins the game. Find their respective probabilities of winning.

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Mathematics>Algebra>Probability>Basics of Probability

A person throws two fair dice. He wins Rs.

15

for throwing a doublet (same numbers on the two dice), wins Rs

12

when the throw results in the sum of

9

, and loses Rs.

6

for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is:

EASY

Mathematics>Algebra>Probability>Basics of Probability

Let

A

and

B

are two mutually exclusive events with

P (A) = \frac{1}{3}

and

P (B) = \frac{1}{4} .

What is the value

P (\bar{A} \cap \bar{B}) ?

If any four numbers are selected and they are multiplied, then the probability that the last digit will 1,3,5 or 7, is

Important Questions on Probability

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