Question

Your friend, Jamie, rolled a number cube and got the number 5. On his next turn, he says he won't be able to roll another 5 because he is only expected to roll a 5 once every six rolls. Is your friend correct? Explain your answer in 2-3 sentences

Answer 1

In fact he could roll 100 sixes in a row.
Of course the probability would be
(1/6)(1/6)(1/6) ...... (1/6) one hundred times = (1/6)^100 = 1.53064671 * 10^-78
which is a pretty low probability (but not impossible)

Answer 2

No, your friend is not correct. Rolling a number cube is an independent event, so the outcome of one roll does not affect the outcome of future rolls. Each roll has an equal probability of rolling a 5, which is 1 out of 6. Therefore, Jamie still has a 1 out of 6 chance of rolling a 5 on his next turn.

Answer 3

You are correct. While the probability of rolling a 5 on a single roll is 1/6, the probability of rolling that same outcome multiple times in a row decreases exponentially. In the case of rolling a 5 one hundred times in a row, the probability is extremely low but still theoretically possible.