During a soccer match of 90 minutes there are 30 fouls on average. How can I calculate the probability of at least one foul at minute x and the probability of at least a foul to happen on an odd minute?
2026-04-06 22:09:40.1775513380
Odd minute Probabililty
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If you have an average of 30 fouls in 90 minutes, then the rate of fouls per minute is $\lambda = 1/3,$ as @N74 says. Then the probability of at least one foul in a particular minute is $$P(X \ge 1) = 1 - P(X=0) = 1- e^{-1/3} = 0.2835,$$ where $X \sim \mathsf{Pois}(\lambda = 1/3).$ In R statistical software:
I have no idea what you mean by at least one foul in an 'odd minute'. Is that a separate problem? Or somehow tangled up with the first part about minute
x? If you mean any odd numbered minute during 90 minutes, unrelated to the above, the rate for that would be $\lambda = 15.$ I'll let you do the rest, depending on what you mean.