Question

The Boston Celtics have won 16 NBA championships over approximately 50 years. Thus is may seemreasonable to to assume that in a given year the Celtics win the title with probability p = 16=50 = 0:32,independent of any other year. Given such a model, what would be the probability of the Celtics winningeight straight championships

Answer 1

0.0001 = 0.01% probability of the Celtics winning eight straight championships.

Explanation:

For each year, there are only two possible outcomes. Either the Celtics are the champions, or they are not. Each year is independent of other years. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

What would be the probability of the Celtics winning eight straight championships?

Each year, we have that
`p = 0.32`

Eight straight championships:
`P(X = 8)` when n = 8. So

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 8) = C_(8,8).(0.32)^(8).(0.68)^(0) = 0.0001`

0.0001 = 0.01% probability of the Celtics winning eight straight championships.