Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-1>Q 20

MEDIUM

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IMPORTANT

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A quadratic equation is chosen from the set of all quadratic equations which are unchanged by squaring their roots. The chance that the chosen equation has equal roots is -

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Important Questions on Probability

HARD

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-1>Q 21

5

persons entered the lift cabin on the ground floor of an

8

floor building. Suppose that each of them independently and with equal probability, can leave the cabin at any other floor, starting from the first. The probability that all

5

persons leave at different floors is -

HARD

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-1>Q 22

If the integers

m

and

n

are chosen at random between

1

and

100,

then the probability that a number of the form

7^{m} + 7^{n}

is divisible by

5,

equals

EASY

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-1>Q 23

There are

10

Prizes, five

A' s,

three

B' s,

and two

C' s,

placed in identical sealed envelopes for the top

10

Contestants in a mathematics contest. The prizes are awarded by allowing winner to select an envelope at random from those remaining. When the

8^{t h}

Contestant goes to select the prize, the probability that the remaining three prizes are one

A,

one

B

and one

C

is,

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-1>Q 24

A & B

are two independent events such that

P (\bar{A}) = 0.7, P (\bar{B}) = a & P (A \cup B) = 0.8

, then

a =

HARD

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-1>Q 25

A determinant is chosen at random from the set of all determinant of order

2

with elements

0

or

1

only. The probability that the determinant chosen has the value non negative is -

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-2>Q 1

If two of the

64

squares are chosen at random on a chess board, the probability that they have a side in common is -

HARD

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-2>Q 2

Let

0 < P (A) < 1, 0 < P (B) < 1

and

P (A \cup B) = P (A) + P (B) - P (A) P (B)

. Then -

HARD

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-2>Q 3

15

coupons are numbered

1, 2, 3, \dots \dots \dots, 15

respectively.

7

coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is

9

is -