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Byju's Answer

Standard XII

Mathematics

Mutually Exclusive Events

In throwing a...

Question

In throwing a dice, let $A$ be the event 'coming up of an odd number', $B$ be the event 'coming up of an even number', $C$ be the event 'coming up of a number $\geq$ 4' and $D$ be the event 'coming up of a number $< 3^{'}$ , then

A

and

B

are mutually exclusive and exhaustive.

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A

and

C

are mutually exclusive and exhaustive.

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A

C

and

D

form an exhaustive system.

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B

C

and

D

form an exhaustive system.

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Solution

The correct options are
A $A$ and $B$ are mutually exclusive and exhaustive.
D $A$ , $C$ and $D$ form an exhaustive system.
Event A has ${1, 3, 5}$
Event B has ${2, 4, 6}$
Event C has ${4, 5, 6}$
Event D has ${1, 2}$
A and B have no element in common, and together they form the universal set for this trial. Hence, A and B are mutually exclusive and exhaustive. Option A is correct.
A and C have $5$ common to them. So they are not exclusive. Option B is incorrect.
A, C and D taken together form the universal set. Hence, they form an exhaustive system. Option C is correct.
B, C and D do not form an exhaustive system because neither of them has $3$ in it. Option D is incorrect.

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Similar questions

Q. In throwing a die. Let

A

be the event ''even number turns up'',

B

be the event ''an odd prime number comes up'' and

C

be the event ''a number less than

4

turns up'', then which of the following events are exhaustive ?

Q. In throwing of a die, let

A

be the event 'even number turns up',

B

be the event 'an odd prime turns up' and

C

be the event 'a number less than

4

turns up'. The events A, B and C form an exhaustive system.

Two dice are thrown. The events A, B, C, D, E and F are described as follows :

A = Getting an even number on the first die.

B = Getting an odd number on the first die.

C = Getting at most 5 as sum of the numbers on the two dice.

D = Getting the sum of the numbers on the dice greater than 5 but less than 10.

E = Getting at least 10 as the sum of the numbers on the dice.

F = Getting an odd number on one of the dice.

(i) Describe the following events : A and B, B or C, B and C, A and E, A or F, A and F

(ii) State true or false :

(a) A and B are mutually exclusive.

(b) A and B are mutually exclusive and exhaustive events.

(d) C and D are mutually exclusive and exhaustive events.

(e) C, D and E are mutually exclusive and exhaustive events.

(f) A' and B' are mutually exclusive events.

(g) A, B, F arc mutually exclusive and exhaustive events.

Q. In throwing a die. Let

A

be the event ''coming up of an odd number'',

B

be the event ''coming up of a number divisible by

2

'',

C

be the event ''coming up of a number

\geq 4

'' and

D

be the event ''coming up of a number

< 3,

then which of the following is/are true?

Q. In throwing a die, which of the following set of events are exhaustive ?

A :

the events ''an odd number turns up'', ''a number

\leq 4

comes up'' and '' the number

5

turns up''.

B :

the events ''a number

\leq 4

turns up'', ''a number

> 4

turns up''.

C :

the events '' an even number turns up'', '' a number divisible by

3

turns up'', '' number

1

2

turns up'' and '' the number

6

turns up''.

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In throwing a dice, let A be the event 'coming up of an odd number', B be the event 'coming up of an even number', C be the event 'coming up of a number ≥ 4' and D be the event 'coming up of a number <3′, then

In throwing a dice, let $A$ be the event 'coming up of an odd number', $B$ be the event 'coming up of an even number', $C$ be the event 'coming up of a number $\geq$ 4' and $D$ be the event 'coming up of a number $< 3^{'}$ , then