In a study of NBA basketball games, it was reported that there are, on average, .3 fouls committed per minute.Assume all the Poisson conditions are met.Determine the probability of no fouls in a randomly selected 2-minute interval.
A).6783
B).7221
C).6109
D).5834
E).5488

Question

Quizplus · Accepted Answer

The Poisson probability formula for exactly x events in an interval is given by $P(X=x) = \frac{e^{-\lambda} \lambda^x}{x!}$, where $\lambda$ is the average rate of success (in this case, fouls) per interval, and $x$ is the number of successes we're interested in. Given that there are on average .3 fouls per minute, in a 2-minute interval, $\lambda = .3 \times 2 = .6$. For no fouls ($x = 0$), the formula simplifies to $P(X=0) = e^{-\lambda} = e^{-.6}$. Calculating $e^{-.6}$ gives approximately .5488, hence the correct answer is E.

In a Study of NBA Basketball Games, It Was Reported