Step by step
The question
Question: each try has a probability of success of 0.05: how many tries do we expect until the first success?
p = 0.05: expected number of tries?
1 The mean
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 0.05 is 20.
μ = 1p = 10.05 = 20
Careful!
0.05 is the chance of one try.
The mean counts tries.
Careful: not μ = 0.05 ✗
2 Check
Let's check: in 20 tries, we expect 20 times 0.05: 1 success.
One success.
So it is right!
20 tries × 0.05 = 1 success
Let's look back.
First: the mean.
Last: check.
Answer
Careful: not μ = 0.05 ✗