Probability of success 0.25, expected number of tries

Step by step, with the reason for every step · The geometric distribution · University Statistics

Step by step

Question: each try has a probability of success of 0.25: how many tries do we expect until the first success?

p = 0.25: expected number of tries?

For tries until the first success, the mean is 1 divided by p.

the mean of a geometric X: μ = 1 ÷ p

1 divided by 0.25 is 4.

μ = 1p = 10.25 = 4

Careful!

0.25 is the chance of one try.

The mean counts tries.

Careful: not μ = 0.25 ✗

Let's check: in 4 tries, we expect 4 times 0.25: 1 success.

One success.

So it is right!

4 tries × 0.25 = 1 success

Let's look back.

First: the mean.

Last: check.

Answer

Careful: not μ = 0.25 ✗

Try this one yourself, then check:

p = 0.5: expected number of tries?

Show the answer

μ = 2