WT, Chapt 5, Problem 3

[Diane.C.Chang]

Hello,

For WT, Chapt 5, Problem 3, it seems there might be a mistake in the book or my mistake.

What is the probability that the sum of two dice will yield a 10 or lower?

There are 4 possibilities of this happening:

D1, D2
5,6
6,6
6,5
6,6

The strategy guide says there are only 3 possibilities. (5+6, 6+5, 6+6). Why is the second instance of 6 + 6 disregarded?

Thanks!

[siddharth.sheth]

This is because both those cases are the same. They are indistinguishable.

Throwing a dice which comes up with a 6 on the first throw, and throwing another dice that comes up with a 6 on the second throw is the same. You can't possibly differentiate them.

On the other hand,throwing a dice and coming up with a 6 on the first throw, and a 5 on the second throw, is DIFFERENT from throwing a dice and coming up with a 5 on the first throw, and a 6 on the second throw.

I hope that makes sense.

Cheers :)

[mikhsor]

could you post what the answer is, please?

[georgepa]

The strategy guide says there are only 3 possibilities. (5+6, 6+5, 6+6). Why is the second instance of 6 + 6 disregarded?

Thanks!

I: Give you two cookies randomly from 2 bags (1 chocolate chip and 1 oatmeal raisin)
You: Take them and stack them together with some cream in the middle to make an Oreo like cookie

How many different Oreo like cookies can you form?

Cookie 1 | Cookie 2
O|C
C|O
O|O
C|C


Here the stacking or filling the center with cream is the same as the addition operation for the pair of dice. You don't count them twice.

[Ben Ku]

D1, D2
5,6
6,6
6,5
6,6

The strategy guide says there are only 3 possibilities. (5+6, 6+5, 6+6). Why is the second instance of 6 + 6 disregarded?

Pretend D1 is red and D2 is white. Your two cases of 6,6 are actually the same. You can't tell the difference, because both the red and white dice are 6's. There are only three possibilities of rolling a sum greater than 10.