Problema Solution
A stoplight at the corner of Lincolnway and Duff Avenue is red 20% of the time. For someone
who drives through this stoplight 10 times a week, what is the probability that
they will have to stop at least one time?
Answer provided by our tutors
each instance of being stopped at the light is an independent event
we are concerned with being stopped "at least" one time, so the events are not mutually-exclusive
there is only one possibility of never being stopped at the light, and that is 10 sequential episodes of not being stopped, so we calculate that probability first
the probability of not being stopped is 80% for any single time and we want to calculate this probability for ten straight events:
(8/10)^10
the probability of being stopped at least once, then, is one minus the probability of never being stopped:
1 - (8/10)^10 = 0.892
there is an 89% probability of being stopped at least one time