If E and F are events with P E ≤ P F and P E ∩ F > 0 , then

none of the above implications holds.

occurrence of E ⇒ occurrence of F

occurrence of F ⇒ occurrence of E

non - occurrence of E ⇒ non - occurrence of F

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In a maths paper there are $3$ sections $A, B & C$ . Section $A$ is compulsory. Out of sections $B & C$ a student has to attempt any one. Passing in the paper means passing in $A$ & passing in $B$ or $C$ . The probability of the student passing in $A, B & C$ are $p, q$ & $1 / 2$ respectively. If the probability that the student is successful is $1 / 2$ then, which of the following is true -

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Important Questions on Probability

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Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-2>Q 19

Sixteen players

S_{1}, S_{2}, \dots \dots \dots, S_{16}

play in a tournament. They are divided into eight pairs at random. From each pair a winner is decided on the basis of a game played between the two players of the pair. Assume that all the players are of equal strength. The probability that "exactly one of the two players

S_{1} & S_{2}

is among the eight winners" is -

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Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-2>Q 20

The number '

a

' is randomly selected from the set

\{0, 1, 2, 3, \dots \dots \dots . 98, 99\}

. The number '

b

' is selected from the same set. Probability that the number

3^{a} + 7^{b}

has a digit equal to

8

at the units place, is -

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Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-2>Q 21

From a pack of

52

playing cards, face cards and tens are removed and kept aside then a card is drawn at random from the remaining cards. If

$A$ : The event that the card drawn is an ace
$H$ : The event that the card drawn is a heart
$S$ : The event that the card drawn is a spade

then which of the following holds?

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Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-2>Q 22

Before a race the chance of three runners

A, B

C

were estimated to be proportional to

5, 3 & 2

respectively but during the race

A

meets with an accident which reduces his chance to

\frac{1}{3}

. If the respective chances of

B

and

C

are

P (B)

and

P (C)

then -

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Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-2>Q 23

E

and

F

are events with

P (E) \leq P (F)

and

P (E \cap F) > 0

, then

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Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-2>Q 24

A

and

B

are two independent events such that

P (A) = \frac{1}{2}

and

P (B) = \frac{1}{5}

, then

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Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-3>Q 12

In a knockout tournament

2^{n}

equally skilled players;

S_{1}, S_{2} . . . . . . . . S_{2^{n}}

are participating. In each round players are divide in pair at random and winner from each pair moves in the next round. If

S_{2}

reaches the semifinal then the probability that

S_{1}

wins the tournament is

\frac{1}{20}

. Find the value of '

n

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Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-3>Q 13

In a multiple choice question there are four alternative answers of which one or more than one is correct. A candidate will get marks on the question only if he ticks all the correct answers. The candidate ticks the answers at random. If the probability of the candidate getting marks on the question is to be greater than or equal to

\frac{1}{3}

, then find the least number of chances he should be allowed.

Important Questions on Probability

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