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If $A & B$ are two events such that $P (B) \neq 1, B^{C}$ denotes the event complementary to $B$ , then -

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Important Questions on Probability

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Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-2>Q 15

The probabilities of events,

A \cap B, A, B & A \cup B

are respectively in

A . P

, with probability of second term equal to the common difference. Therefore, the events

A

and

B

are -

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Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-2>Q 16

From an urn containing six balls,

3

white and

3

black ones, a person selects at random an even number of balls (all the different ways of drawing an even number of balls are considered equally probable, irrespective of their number). Then, the probability that there will be the same number of black and white balls among them, is

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Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-2>Q 17

A pair of fair dice having six faces numbered from

1

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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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 -

If A & B are two events such that PB≠1, BC denotes the event complementary to B, then -

Important Questions on Probability

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If $A & B$ are two events such that $P (B) \neq 1, B^{C}$ denotes the event complementary to $B$ , then -