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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IMPORTANT

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A pair of fair dice having six faces numbered from $1$ to $6$ are thrown once, suppose two events $E$ and $F$ are defined as -
$E$ : Product of the two numbers appearing is divisible by $5 .$

$F$ : At least one of the dice shows up the face one.

Then the events $E$ and $F$ are

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Important Questions on Probability

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Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-2>Q 18

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

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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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

A pair of fair dice having six faces numbered from 1 to 6 are thrown once, suppose two events E and F are defined as - E : Product of the two numbers appearing is divisible by 5. F : At least one of the dice shows up the face one. Then the events E and F are

Important Questions on Probability

Learn and Prepare for any exam you want !

A pair of fair dice having six faces numbered from $1$ to $6$ are thrown once, suppose two events $E$ and $F$ are defined as -
$E$ : Product of the two numbers appearing is divisible by $5 .$

$F$ : At least one of the dice shows up the face one.

Then the events $E$ and $F$ are