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Bethany has two fair six-sided dice that she throws. She defines $N$ as the product of his two numbers.

Find $P (N is odd)$ .

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Important Questions on Probability

MEDIUM

Mathematics>Algebra>Probability>Probability of an Event

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>Probability of an Event

The probability that among

7

persons, no

2

were born on the same day of a week is

HARD

Mathematics>Algebra>Probability>Probability of an Event

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:

MEDIUM

Mathematics>Algebra>Probability>Probability of an Event

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

HARD

Mathematics>Algebra>Probability>Probability of an Event

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>Probability of an Event

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>Probability of an Event

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>Probability of an Event

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>Probability of an Event

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>Probability of an Event

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>Probability of an Event

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 ?

HARD

Mathematics>Algebra>Probability>Probability of an Event

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>Probability of an Event

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>Probability of an Event

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 :

HARD

Mathematics>Algebra>Probability>Probability of an Event

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>Probability of an Event

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>Probability of an Event

There are 6 boxes labelled

B_{1}, B_{2}, \dots ., B_{6} .

In each trial, two fair dice

D_{1}, D_{2}

are thrown. If

D_{1}

shows j and

D_{2}

shows

k

, then

j

balls are put into the box

B_{k} .

After

n

trials, what is the probability that

B_{1}

contains at most one ball?

HARD

Mathematics>Algebra>Probability>Probability of an Event

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:

EASY

Mathematics>Algebra>Probability>Probability of an Event

Two cards are drawn at random and one-by-one without replacement from a well-shuffled pack of

52

playing cards. Find the probability that one card is red and the other is black.

MEDIUM

Mathematics>Algebra>Probability>Probability of an Event

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

Bethany has two fair six-sided dice that she throws. She defines N as the product of his two numbers. Find P(N is odd).

Important Questions on Probability

Learn and Prepare for any exam you want !

Bethany has two fair six-sided dice that she throws. She defines $N$ as the product of his two numbers.

Find $P (N is odd)$ .