Analyzing Theoretical Probability with Dice?

Question

The six faces on a number cube have the numbers from 1 to 6 shown on them. If you roll one number cube, your chances of rolling the number 5 are 1 in 6 or 1/6. If you roll two number cubes, your chances of rolling a 5 increase. You would think that your chances would be 1/6 for each number cube, or 1/6 + 1/6 or 1/3 when you roll two. The more number cubes that you roll, the better your chances become. For example, you might think that when you roll six number cubes, your chances of rolling a 5 are 1/6 x 6, or 1. But a probability of 1 means that you would always roll a 5 when you roll six number cubes. You should know that this is not true. What went wrong?

Look over the assumptions that were made to find one or more that were wrong. Then show how or why it or they were wrong. -- I've been rereading and trying this problem for 45 minutes now but am completely stumped. Could someone please help me out?

Answer 1

The chance of getting a 5 on either number cube is 2/12 (there are two 6's out of 12 numbers), which is still 1/6.

When six number cubes are rolled, the chance of rolling one five is 6/36, or 1/6. The chance of rolling all fives is (1/6)^5, or 1/7776.

Answer 2

If you roll one die, your chances of rolling a 5 are 1 / 6

if you roll 2 dice, your chances of rolling a 5 are 2 / 12, still 1/6
because a possible 12 different numbers can be rolled
1,2,3,4,5,6,1,2,3,4,5,6
and only 2 of those can be 5

with 3 dice, you chances are 3/18, still 1/6

and so on

Answer 3

There is probably a rounding thing going on. How about you find the odds of rolling six dice and not getting a five. Subtract that from a probability of one and viola you have your odds

Answer 4

It's the theory of probability, not the FACT of probability. It doesn't mean you will get it every time.