Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-1>Q 7

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IMPORTANT

Earn 100

Three of the six vertices of a regular hexagon are chosen at random. Then the probability that the triangle with three vertices is equilateral is $' p'$ then $100 p$ equals

Important Questions on Probability

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-1>Q 8

In throwing a pair of dice, find whether the two events

(i) E_{1}

: 'coming up of an odd number on first dice' and

E_{2}

: 'coming up of a total of

8

'.

(i i) E_{1}

: 'coming up of

4

on first dice' and

E_{2}

: 'coming up of

5

on the second dice'.
are mutually exclusive or not.

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-1>Q 10

Before race the chance of three runners,

A, B, C

were estimated to be proportional to

5, 3, 2,

but during the race

A

meets with an accident which reduces his chance to

\frac{1}{3} .

What are the respective chance of

B

and

C

now?

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Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-1>Q 11

Tickets are numbered from

1

to

100 .

One ticket is picked up at random. Then find the probability that the ticket picked up has a number which is divisible by

5

or

8 .

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Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-1>Q 12

Three cards are drawn at random from a pack of well shuffled

52

cards. Find the probability that all the three cards are of the same suit;

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Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-1>Q 13

In a throw of a pair of dice, then find the probability of '

A

total of

8

but not

11

'.

HARD

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Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-1>Q 14

Six boys and six girls sit in a row at random. Find the probability that the boys and girls sit alternatively.

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Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-1>Q 16

Four persons draw four cards form an ordinary pack of

52

cards. Find the probability that no two cards are of equal value.

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Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-1>Q 17

Prove that

P (A - B) = P (A) - P (A \cap B) = P (A \cup B) - P (B) = P (A \cap \bar{B}) = 1 - P (\bar{A} \cap B)