Two dice are thrown. The events A, B and C are as follows:

A: getting an even number on the first die.

B: getting an odd number on the first die.

C: getting the sum of the numbers on the dice ≤ 5

State whether the following is true or false (give reason for your answer):
A and B' are mutually exclusive.

Two dice are thrown. The events A, B and C are as follows:

A: getting an even number on the first die.

B: getting an odd number on the first die.

C: getting the sum of the numbers on the dice ≤ 5

State whether the following is true or false (give reason for your answer):
A', B' C are mutually exclusive and exhaustive.

From a group of 2 boys and 3 girls, two children selected at random. Describe the events:

A : Both children are girls.

B : The selected group consists of one boy and one girl.

C : The group consists of atleast one girl.

Find: (a) Events: B', C - A, A ∪ B,B ∩ C.

(b) Which pairs of events are mutually exclusive?

One die is rolled. Define the sample space S of the following:

A : Getting a prime number

B : Getting an odd number

C : Getting a number less than 5

D : Getting a number divisible by 3

Use the sample space and above sets to find:

(i) A ∩ B (ii) B' (iii) C' ∩ D

(iv) A ∪ B (v) C ∩ D

Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experiment:

A : The sum is even

B : The sum is multiple of 3

C : The sum is less than 4

D : The sum is greater than 11.

Which pairs of these events are mutually exclusive?

A coin is tossed three times. Consider the following events:

A : No head appears

B : Exactly one head appears.

C : At least two heads appear

Do they form set of mutually exclusive and exhaustive events?

A die is rolled once and the following events are described:

A : Getting a prime number on the die.

B : Getting an even number on the die.

Write the sets representing the following events.

(a) A ∩ B    (b) A ∪ B       (c) A-B

(d) A' ∩ B'   (e) A ∪ B'

Three coins are tossed (or one coin is tossed thrice). The following events are described:

A : Getting atleast one head.

B : Getting atmost one head. Write the sets representing the following events:

(a) A ∪ B (b) A ∩ B (c) A - B

(d) A' - B.

Which of the events is a sure event and which one is impossible event ?

419.

Two dice are rolled and the sum of numbers on them is noted. Events A, B, C, D are described as follows:

A : The sum is even.

B : The sum is a multiple of 4.

C : The sum is less than 6.

D : The sum is greater than 10.

Which pairs of the events are mutually exclusive?

A : Getting a sum 10

B : Getting a sum 11

C : Getting a sum 12

(i) Is event B simple? (ii) Is event C simple? (iii) Is event A compound?

Are events B and C mutually exclusive?