Assume you take the bus to campus. About every 5 times (1 in 5) you take the bus in the morning it is full when it comes to your stop and it takes no more passengers. This means that you have to wait for the next available bus. To your surprise, 3 days in a row the bus is full when it comes to your stop. Based on your previous estimate, what is the probability of this happening?
one in five (.2)
.2 is the probability of it happening once. The probability of it happening 3 times in a row = .2^3 = .2*.2*.2 = .008.
To find the probability of the bus being full when it comes to your stop three days in a row, we need to calculate the probability of each event occurring and then multiply them together.
Given that the bus is full 1 in every 5 times (1/5) you take it, the probability of the bus being full on any given day is 1/5.
So, the probability of the bus being full for three consecutive days is:
(1/5) * (1/5) * (1/5) = 1/125
Therefore, the probability of the bus being full when it comes to your stop for three consecutive days is 1/125.
Keep in mind that this calculation assumes that each day's bus capacity is independent of the previous day, which may not be the case in reality.