Question of the day
2026-09-26
Brain Teasers
Roll a single die. If it lands on 6, you roll again and add; you keep rolling and adding as long as you roll a 6. What is the expected total?
Answer it out loud first — like you would in the room. Then check yourself:
Reveal the model answer
Model answer
Let E be the expected total. E = (1/6)(1+2+3+4+5) + (1/6)(6 + E) = 15/6 + 1 + E/6. So E − E/6 = 15/6 + 1 = 21/6, giving (5/6)E = 7/2, E = 21/5 = 4.2. The re-roll on 6 pulls the mean above the ordinary 3.5.
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