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I got stuck by this sentence:

What is the probability of rolling a six on two consecutive rolls of a fair six-sided die?

I thought it would just be a binomial random variable problem, where only one occurrence of six would be OK, but found that it is asking for a joint probability which means that both two rolls should show six.

Why does "a six on two consecutive rolls" mean two sixes rather than one(a)?

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  • Because you are talking about single action (rolling a six) that occurs on more than one occasion. Contrast that with a situation if you had two dice: "What is the probability of rolling two sixes on consecutive rolls?"
    – Karen927
    May 24, 2019 at 1:02

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Short answer: Consecutive means "one after the other."

In general we can say that

Outcome X happened Y consecutive times

means that, when doing a repeating action, the outcome was X the first time, then it was repeated and the outcome was again X, then again X, etc. And this happened Y times in a row without any other outcome happening in between.

We can thus rewrite your sentence as

What is the probability that, when rolling a fair six-sided die twice, we get a roll of 6 both times?

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  • It would have been clearer if the sentence had been written with "consecutive" modifying "sixes" instead of "rolls".
    – Lorel C.
    May 24, 2019 at 0:47

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