Question

You are visiting San Francisco and are taking a trolley ride to a store on Market Street. You are supposed to meet a friend at the store at 3:00 P.M. The trolleys run every 10 minutes and the trip to the store is 8 minutes. You arrive at the trolley stop at 2:48 P.M. What is the probability that you will arrive at the store by 3:00 P.M.?

• A. 30%
• B. 20%
• C. 60%
• D. 40%

Answer 1

The correct option is D 40%

To begin, find the greatest amount of time you can afford to wait for the trolley and still get to the store by 3:00 P.M.

Because the ride takes 8 minutes, you need to catch the trolley no later than 8 minutes before 3:00 P.M., or in other words by 2:52 P.M.

So, you can afford to wait 4 minutes (2:52 - 2:48 = 4 min).

If the trolley doesn't come in first 4 minutes then we have to wait for 10 minutes to get a trolley ride. So we won't be able to reach to the store on time.

You can use a line segment to model the probability that the trolley will come within 4 minutes.


P(Get to store by 3:00) = $$\frac{Favourablewaitingtime}{Maximumwaitingtime}$$=$\frac{4}{10}$=$\frac{2}{5}$

The probability is $\frac{2}{5}$, or 40%.