Question

Suppose you roll a six-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

wouldnt it be 18/36

Answer 2

i just need clarification

Answer 3

@AriPotta
those possibilities are not equally likely

Answer 4

it is true that the sample space is { 2,3,4,5,6,7,8,9,10,11,12} , but the sample points are not equally likely.

Answer 5

you want to know probability of rolling a sum of 2,4,6,8,10,12
you can use a diagram of the sum of two die , we can google an image

Answer 6

P( roll 2) = 1/36
P(roll 4) = 3/36
P( roll 6) = 5/36
P(roll 8) = 5/36
P( roll 10) = 3/36
P( roll 12) = 1/36

now add up these probabilities

Answer 7

18/36?

Answer 8

or 1/2

Answer 9

would that be the sample space or number of favorable outcomes

Answer 10

I used the modified sample space , weighting the sample points

Answer 11

so what would be the number of favorable outcomes?

Answer 12

@perl

Answer 13

if you want to use the original 36 point sample space, then you would have
18 favorable, and 36 total

Answer 14

original 36 point sample space
S = { (1,1) (1,2) (2,1) (1,3) (2,2) (3,1) ...}

Answer 15

then the favorable events are
(1,1) (1,3) (2,2) (3,1) ... those that add to an even number