## Related questions with answers

"The Fountains of Bellagio" is a choreographed water display set to light and music that takes place in front of the Bellagio Hotel in Las Vegas. In the evening, the shows take place every 15 min from 7 p.m. to midnight. The duration of each show is 7 min. If Joan arrives at a random time between 7 P.M. and 7:15 P.M. for an evening show and finds the fountains not performing, find the probability that Joan will have to wait at most 5 min before the next show starts.

Solution

VerifiedLike in Example $4$,label with $X$ the time that Joan has to wait for the next show.

$X$ is uniformly distributed over the interval $\left[0,8 \right]$ and our uniform density function is $f(x)=\frac{1}{8}$.

Now we have:

$\begin{align*} P(0\leq X \leq 5)&=\int_{0}^{5} {\frac{1}{8} dx}\\ &=\left[ \frac{1}{8}x \right]_{x=0}^{x=5}\\ &=\boldsymbol{\frac{5}{8}} \\ \end{align*}$

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