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Earn 100

Consider the system of equations $a x + b y = 0$ and $c x + d y = 0$ where $a, b, c, d \in [1,2] .$

The probability that the system of equations has a unique solution is

50% studentsanswered this correctly

Important Questions on Probability

EASY

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

HARD

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 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:

HARD

Mathematics>Algebra>Probability>Basics of Probability

Three randomly chosen non negative integers

x, y, z

are found to satisfy the equation

x + y + z = 10

. Then the probability that

z

is even, is

EASY

Mathematics>Algebra>Probability>Basics of Probability

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.

HARD

Mathematics>Algebra>Probability>Basics of Probability

Three boys and two girls stand in a queue. The probability that the number of boys ahead of every girl is at least one more than the number of girls ahead of her, is

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

If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral 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

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 :

MEDIUM

Mathematics>Algebra>Probability>Basics of 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?

HARD

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

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 :

EASY

Mathematics>Algebra>Probability>Basics of 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?

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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?

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Mathematics>Algebra>Probability>Basics of Probability

10

different balls are to be placed in

4

distinct boxes at random, then the probability that two of these boxes contain exactly

2

and

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

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:

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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?

Consider the system of equations ax+by=0 and cx+dy=0 where a,b,c,d ∈1,2. The probability that the system of equations has a unique solution is

Important Questions on Probability

Learn and Prepare for any exam you want !

Consider the system of equations $a x + b y = 0$ and $c x + d y = 0$ where $a, b, c, d \in [1,2] .$

The probability that the system of equations has a unique solution is