Question

Here are the possible outcomes when a pair of fair dice is rolled.

1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12


In a roll of a pair of fair dice, what is the probability of the outcome being either a multiple of 3 or an even number? Are these events mutually exclusive?
, mutually exclusive
, not mutually exclusive
, mutually exclusive
, not mutually exclusive

Answer 1

I don't understand the big table of numbers at the top at all,
and don't see how it relates to the question.


There are 36 possible outcomes for the roll of a pair of dice.
According to your specifications, the successes are:

-- Multiples of 3:
1 ... 2 (3)
2 ... 1
3 ... 3 (6)
1 ... 5
5 ... 1
2 ... 4
4 ... 2
3 ... 6 (9)
6 ... 3
4 ... 5
5 ... 4
6 ... 6 (12)
(12 different outcomes)

-- Even numbers:
1 ... 1 (2)
1 ... 3 (4)
3 ... 1
2 ... 2
3 ... 3 (6)
1 ... 5
5 ... 1
2 ... 4
4 ... 2
2 ... 6 (8)
6 ... 2
3 ... 5
5 ... 3
4 ... 4
4 ... 6 (10)
6 ... 4
5 ... 5
6 ... 6 (12)
(18 different outcomes)

The events are NOT mutually exclusive.
A roll of 6 (5 ways) or 12 (1 way) meets both requirements.

Successful outcomes:
Multiples of 3 . . . . 12
Even numbers . . . 18
Duplicates . . . . 6

So there are 24 different successful outcomes.

Probability = (24) / (36) = 2/3 = (66 and 2/3) %