Question

A pair of dice is rolled. What is the probability that the sum of the numbers rolled is either an even number or a multiple of 3?

Answer 1

I have the answer, and I mostly know how to do it; I just have one question.

Answer 2

Because it is not mutually exclusive, to calculate this I use this
P(even) + P(multiple of 3) - P(6)
But according to the site I got this there are 6 ways of rolling a six, not 5 which is what I got

Answer 3

6
1-5
2-4
3-3
4-2
5-1

Answer 4

Unless it is counting 3-3 twice

Answer 5

Am I supposed to count 3-3 twice?

Answer 6

I don't think so. there is only one way to roll a 3-3

Answer 7

This is their explaination:

Of the 36 possible outcomes, 18 are even sums.
P(even) = 18/36 = 1/2

Sums of 3, 6, 9, and 12 are multiples of 3.
There are 12 sums that are multiples of 3.
P(multiple of 3)= 12/36 = 1/3

However, some of these outcomes appear in both events.
(not mutually exclusive)
The sums that are even and a multiple of 3 are 6 and 12.
There are 6 ordered pairs with these sums.
P(even AND a multiple of 3) = 6/36 = 1/6

P(even OR a multiple of 3) = 18/36 + 12/36 - 6/36 = 24/36 = 2/3

Answer 8

Oh sorry

Answer 9

Probability of rolling a 6 AND 12, forgot about the twelve

Answer 10

Whats the difference between mutually inclusive and mutually exclusive?

Answer 11

Mutually exclusive means both events can't happen at the same time.

Answer 12

Thank you, I think I understand the difference.

Answer 13

A silly eample of mutually exclusive is if you were asked to pick a number from 1 to 10. What's the probability it will be an odd number of a multiple of 2. There are 5 odd numbers from 1 to 10 and there are 5 multiples of 2 from 1 to 10. You add the probabilities The two choices are mutually exclusive bec if a nunmber is a multiple of 2, it is even, and it can't be odd.

Answer 14

You're welcome.