Question

Two Fair die are rolled. What is the probability of one of the dice showing 5 or the sum being at least 8?

Answer 1

write down the cases in which the sum can be 8 with one of them being 5

Answer 2

okay should I include (5,3) and (3,5)

Answer 3

or no repeats

Answer 4

you include both

Answer 5

okay I did that

Answer 6

arent you getting the answer?

Answer 7

it says a sum of at least 8

Answer 8

oops yeah so inluse(5,4) (4,5), (5,5) (5,6)(6,5)

Answer 9

okay I did that and there are a total 15 ways to make a sum of at least 8

Answer 10

"okay I did that and there are a total 15 ways to make a sum of at least 8"
That is correct. It is necessary to avoid double counting, therefore the next step is to find out how many occurrences of 5 there are on one of the dice where the sum of the numbers on the pair is less than 8.

Answer 11

There are two, but does (5,5) count or no because its on two die?

Answer 12

There are more than two. Also (5, 5) does not count because it is already in the total of the 15 ways to make at least 8.

Answer 13

are there four?

Answer 14

Yes, four: (2, 5) (1, 5) (5,2) (5,1).

Answer 15

okay, so now what?

Answer 16

So the total number of ways to get one of the dice showing 5 or the sum being at least 8 (without double counting) is 15 + 4 = 19 ways.
What is the value of the sample space?

Answer 17

what do you mean the value of the sample space?

Answer 18

The sample space has 36 possible combinations of numbers.

Answer 19

oh okay. Now i know what you mean

Answer 20

so its 19/36?

Answer 21

Yes, you are correct.

Answer 22

OMG thank you so much, I've been stuck on that problem for over an hour :D. You are a lifesaver xD

Answer 23

You're welcome :)