Question

You roll two standard number cubes. What is the probability that the sum is even, given that one number cube shows a 2?

Answer 1

did you list all the possibilities pairs that has 2?

Answer 2

no....

Answer 3

well are you going to?

Answer 4

1,1 1,2 1,3 1,4 1,5 1,6
2,1 2,2 2,3 2,4 2,5 2,6
3,1 3,2 3,3 3,4 3,5 3,6
4,1 4,2 4,3 4,4 4,5 4,6
5,1 5,2 5,3 5,4 5,5 5,6
6,1 6,2 6,3 6,4 6,5 6,6
so probability of at least one cube shows a 2 is 11/36.

Answer 5

It says "given that one number cube shows a 2", so let's assume that it's the first number cube that shows a 2.

If that's the case, then we look at row 2 which is

2,1 2,2 2,3 2,4 2,5 2,6

now what are the sums of each pair?

Answer 6

3,4,5,6,7,8

Answer 7

which of those sums are even?

Answer 8

all possible pairs that has 2 is:
(1,2)
(2,1)
(2,2)
(2,3)
(3,2)
(2,4)
(4,2)
(2,5)
(5,2)
(2,6)
(6,2)

So there are 11. Out of those 11 pairs, which one has the sum of even?

Answer 9

(2,2)
(2,4)
(4,2)
(2,6)
(6,2)

Answer 10

so that would be 5/11

Answer 11

my book says 1/2.......

Answer 12

but i dont see how

Answer 13

If the first die is 2, then we have this set of possibilities

2,1 2,2 2,3 2,4 2,5 2,6

They add to: 3, 4, 5, 6, 7, 8

Of that list, only 4, 6, 8 are even. This is 3 sums out of 6

so, 3/6 = 1/2 is your answer

Answer 14

Then the question assume only ONE of the cube shows 2. Show the pair (2,2) wasn't not supposed to be counted.

So answer is indeed 5/10 = 1/2

Answer 15

But really, the book wasn't being specific because such phrase "given that one number cube shows a 2" actually means AT LEAST one.

Answer 16

so i only needed 1 die with a 2 on it not both of them

Answer 17

Yes, in this case. Sometimes the misuse of language can change the meaning of a question. But as long as it's not a conceptual misunderstanding, then you'll be fine.

Answer 18

ty @jim_thompson5910 @@sourwing