Probability?

Question

Julie throws a fair red dice once and a fair blue dice once.
Calculate the probability that Julie gets a six on both the red dice and blue dice.
Secondly, calculate the probability that Julie gets at least one six.

Answer 1

both: 1/36 one: 1/6

Answer 2

For the first probability, you multiply the separate probablilites:

Six on both die: 1/6 * 1/6 = 1/36

This is like saying "The probability of a AND the probability of b."

For the second probability, you subtract the chance of getting no sixes from one:

Six on either die: 1 - (5/6 * 5/6) = 11/36

This is like saying "The probability of a OR the probability of b."

Answer 3

1/36 11/36

Answer 4

Fifty-fifty each roll. If I'm wrong I'll apologize. But I seem to recall reading that you could roll a six (or any number) a thousand times and the next roll's odds are unchanged.
Technically true, maybe, but our gut feeling gives it the lie, n' est ce pas?

Answer 5

1/6, 1/6