Question

A wheel at a carnival game has 30
sectors of equal size, with 15
red sectors ​and 15
black sectors.
​
​At the end of a spin of the wheel, the pointer is equally ​likely to land on a red sector or a black sector.
​
​A boy observes four ​consecutive red spins and guesses the next spin will be red.
​
​When asked ​why, he says the wheel is on a “hot streak of red.”
​
​Is his reasoning ​accurate? Why or why not?

Answer 1

Not really. If the wheel is fair and each spin is independent, the chance the next spin is red is still 15/30 = 1/2, no matter what happened before. Four reds in a row has probability (1/2)^4 = 1/16 (6.25%) — uncommon but not impossible — and does not by itself change the probability of the next independent spin.

(Clarification: believing a run makes the same outcome more likely is the “hot‑hand” fallacy. The opposite belief — that a run makes the opposite outcome more likely — is the gambler’s fallacy. Both ignore independence. The only time the past should change your prediction is if the run makes you suspect the wheel is biased; in that case a Bayesian update is appropriate.)