Question

Michael Jordan, the greatest basketball player ever, made 80% of his free throws. In a game what is the expected number he would make before his first miss

1. The expected number Michael Jordan would make before his first miss is 4.

### What is probability?

• Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true.
• The probability of an event is a number between 0 and 1, where 0 indicates the event’s impossibility and 1 indicates certainty.
To find what the expected number Michael Jordan would make before his first miss:
Here is an example where we want the number of successes before the first failure.
• Using the neutral language of heads and tails: success is tails (probability 1−p) and failure is headed (probability = p).
• Therefore p = .2 and the number of tails (made free throws).
• before the first heads (missed free throw) is modeled by an X ∼ geo(.2).
So,
• E(X) = 1 – p / p = .8 / .2 = 4.
Therefore, the expected number Michael Jordan would make before his first miss is 4.