Three ones in a row

A fair die is rolled $5$ times. What is the probability of getting at least $3$ consecutive $1$ s somewhere in the five rolls?

Show hints (2)+

Mark rolls as one ( $O$ ) / not-one ( $X$ ); count length- $5$ patterns with a run of $\ge 3$ $O$ s, weighting each $X$ by $5$ outcomes.
The favorable ordered outcomes total $96$ out of $6^5=7776$ .

Answer

Reveal answer →

0.0123 (± 0.0005)

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