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Standard XIII

Mathematics

Exhaustive Events

Let sample sp...

Question

Let sample space, S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Let us define the following events
A: "set of numbers divisible by 2".
B: "set of numbers divisible by 3".
Then what should be the event C such that events A, B and C are mutually exhaustive?

{1, 6, 9}

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{1, 5, 7}

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{7, 0, 5}

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{4, 8, 9}

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Solution

The correct option is B {1, 5, 7}
A = {2, 4, 6, 8, 10}
B = {3, 6, 9}
$\Rightarrow A \cup B = {2, 3, 4, 6, 8, 9, 10}$
Events A, B and C are mutually exhaustive when $A \cup B \cup C = S So, C = S - (A \cup B) Therefore, C = {1, 5, 7}$

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Similar questions

Q. Let sample space, S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Let us define the following events
A: "set of numbers divisible by 2".
B: "set of numbers divisible by 3".
Then what should be the event C such that events A, B and C are mutually exhaustive?

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''.

Q. Let

A

denote the event that a

6

-digit integer formed by

0, 1, 2, 3, 4, 5, 6

without repetitions, be divisible by

3.

Then probability of event

A

is equal to :

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

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'' and

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be the event ''coming up of a number

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then which of the following is/are true?

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Let sample space, S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Let us define the following events A: "set of numbers divisible by 2". B: "set of numbers divisible by 3". Then what should be the event C such that events A, B and C are mutually exhaustive?

The correct option is B {1, 5, 7}A = {2, 4, 6, 8, 10} B = {3, 6, 9} ⇒A∪B = {2, 3, 4, 6, 8, 9, 10} Events A, B and C are mutually exhaustive when A∪B∪C=SSo, C=S−(A∪B)Therefore, C = {1, 5, 7}

Let sample space, S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Let us define the following events
A: "set of numbers divisible by 2".
B: "set of numbers divisible by 3".
Then what should be the event C such that events A, B and C are mutually exhaustive?

The correct option is B {1, 5, 7}
A = {2, 4, 6, 8, 10}
B = {3, 6, 9}
$\Rightarrow A \cup B = {2, 3, 4, 6, 8, 9, 10}$
Events A, B and C are mutually exhaustive when $A \cup B \cup C = S So, C = S - (A \cup B) Therefore, C = {1, 5, 7}$