Question

You roll 2 dice. What is the probability that the sum of the dice is greater than 8 and that 1 die shows a 6?

Answer 1

Is it 7/36?

Answer 2

No. How did you solve it?

Answer 3

Oh man, used the table of dice outcomes but it confuses me.

Answer 4

If you get a 6 on the first dice then for getting a sum greater than 8, you need to get a number greater than 2 on the second dice (since 6 + 2 = 8) Hence you can get a 3, 4, 5 or a 6 on the second dice. Thus the combinations matching the given conditions are :

(6, 3), (6, 4), (6, 5) and (6, 6)

Four favorable outcomes out of 36 total outcomes

Answer 5

Oh okay, what I did was include the ones you just said (6, 3), (6, 4), (6, 5) and (6, 6), but also (3, 6), (4, 6), and (5, 6) for a total of 7/36. I don't know why I did that. Thanks for your help!

Answer 6

Great! The question states clearly that you get a 6 on dice 1 so the 6 must be on the first dice only!

Answer 7

Oh okay, I thought it meant that either one of the two die could have the 6.

Answer 8

Wait.. just reread the question.. sorry the question says that "1 die shows a 6" not that "die 1 shows a 6" so you are correct. Again sorry!

"1 die shows a 6" means any of the two dice can show a 6. If it would be "die 1 shows a 6" that would mean only the first die.

So your answer 7/36 is correct!

Answer 9

Oh I see, it's okay. Thanks for verifying my answer.