Question

Suppose you roll an eight-sided die two times hoping to get two numbers whose sum is even. What is the sample space? How many favorable outcomes are there?

Answer 1

your sample will be a pair {x,y} drawn from the pair of sets {1.2.3.4.5.6.7.8}{1,2,3,4,5,6,7,8} ... but the order doesn't matter.

Suppose you have a pair, each of which can be Even (E) or Odd (O). What is:
E + E
E + O
O + E
O + O

?

Answer 2

i wanted to ask if the total possible outcomes would be out of 16 since you are rolling the 8-die twice...or is it just out of 8?

Answer 3

No - the way you combine independent events is to multiply them

For each number that comes up first, you can get any one of the 8 coming up next

Answer 4

So you can get {1,1} {1,2} .... up to {1,8}
then {2,1} {2,2} .... {2,8}

etc

Answer 5

oh okay the way the question is worded had me kind of confused at to what to do but i get it now

Answer 6

Good ... so how many outcomes are there ?

Answer 7

we have 8 outcomes if we roll same number twice, if you roll {1,3} and {3,1} do we count them as a distinct outcomes?

Answer 8

No, they are seperate - we are going to add them together, so it doesnt matter which way they come up

If it did matter, we would have 8x8 outcomes. Because it doesnt matter, we only have 32, because we can swap them around and the sum is the same

Answer 9

oh okay that is the same amount of outcomes i got too

Answer 10

Good - now how many of those will be SUCCESSFUL

ie Even?

Answer 11

i got 16 outcomes will be successful