From: Peggy, a teacher

This question is posed in a grade 7 math text and I can't get the answer.

The school bus arrives at Janet's stop on time on 75% of school mornings. What is the probability it will arrive on time each day in a 5-day week?

Hi Peggy.

When you are dealing with independent events, you multiply the probabilities together.

So the probability that on Monday the bus will be on time is 75%. On Tuesday the probability that on Monday the bus will be on time is 75%, etc. They are independent.

Let's look at each day in succession. As soon as the bus is late, we stop looking (we don't care how many times it is late in the week).

On Monday, there's a 75% chance it is on time and 25% that it is late (if it is, stop here).

There's a 75% chance we are even going to look at Tuesday. Say we do, then there is a 75% 75% chance we'll look at Wednesday, etc. By the time we think about looking at Saturday, we've reached (75%)⁵ = 0.75⁵. This is the same as just multiplying the events together, but I wanted to show you why it makes sense to do so.

Hope this helps!
Stephen La Rocque.