Number Properties - 5th ed - page 65

[michel.seguin]

My question is concerning problem one of the problem set: What is the probability that the sum of two dice will yield a 10 or lower?

I think I disagree with the solution. Two roll greater than 10, possible outcomes are: 4-6, 6-4, 6-6, 6-6. Correct?

I don't understand why the solution only counts 6-6 once? If that's the case, than why do we count both 4-6 and 6-4 ? Isn't that just taking into account that dice 1 could roll a 4 and dice 2 roll a 6 and vice versa? Then the same logic could be applied to 6-6. Dice one rolls six, dice two rolls six, then vice versa?

Thanks for any comments. Perhaps I'm just over thinking this!

Mitch

[jnelson0612]

Michael, good question. This concept has been discussed here before; check out the last two posts of this thread: probability-strategy-questions-1-3-t1813.html

[WilliamB970]

I looked at the explanations on the link jnelson0612 provided. The question asked there may be similar but that explanation didn't help me. What you need to do is visualize all 36 of the possible outcomes to see that (6, 6) isn't being counted twice. Here are the 36 possibilities:

[RonPurewal]

just imagine that one die is, say, orange and the other is blue.

you can get an orange 4 and a blue 6, or a blue 4 and an orange 6.

on the other hand, there is only one way to get a blue 6 and an orange 6.