Consider the type of clothes dryer gas or electric purchased

Consider the type of clothes dryer (gas or electric) purchased
by each of five different customers at a certain
store.
a. If the probability that at most one of these purchases an
electric dryer is .428, what is the probability that at least
two purchase an electric dryer?

I know the answer is A\' because that\'s on chegg, but I want to know why is it A\'. If P(A) is the probability that at most 1 electric dry is build, how is P(A\') the probability that at least 2 is bought? What is the logic behind this?

(My first Statistics Class)

Solution

We have 5 people

Atmost one ---> 0 people or 1 people

Atleast 2 ---> 2 people or 3 or 4 or all 5 people

P(0) + P(1) + P(2) + P(3) + P(4) + P(5) = 1

Now, P(0) + P(1) is P(atmost 1)

And P(2) + P(3) + P(4) + P(5) is P(atleast 2)

Substituting this :

P(atmost 1) + P(atleast 2) = 1

So, P(atmost 1) = 1 - P(atleast 2)

This is how it works out