An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:
A: the sum is greater than 8,

B: 2 occurs on either die

C: the sum is at least 7 and a multiple of 3.

Which pairs of these events are mutually exclusive?

Question

Philoid · Accepted Answer

Since a pair of dice is thrown, all the possible outcomes or sample space (S) will be as follows

A: the sum is greater than 8

Possible sum greater than 8 are 9, 10, 11 & 12

∴ A=

B: 2 occurs on either die

Here possibilities are there that the number 2 will come on first die or second die or both the die simultaneously

B=

C: The sum is at least 7 and multiple of 3

So the sum can be only 9 or 12

C=

For 2 elements to be mutually exclusive, then there should not be any common element amongst them

(i) A∩ B =ϕ

As there is no common element in A and B

So A& B are mutually exclusive

(ii) B ∩ C = ϕ

Since there is no common element between

So B and C are mutually exclusive.

(iii) A ∩ C

⇒ ≠ ϕ

Since A and C has common elements,

∴ A and C are mutually exclusive.

An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:A: the sum is greater than 8,B: 2 occurs on either dieC: the sum is at least 7 and a multiple of 3.Which pairs of these events are mutually exclusive?