If approximately 12% of people have coulrophobia, what is the probability that at least one person in a random sample of ten people has this condition?

To find the probability that at least one person in a random sample of ten has coulrophobia, we can use the complement rule. The complement of at least one having the condition is that none of the ten people have it.

Given that 12% of people have coulrophobia, this means that the probability that a person does not have it is 1 - 0.12 = 0.88.

The probability that all 10 people in the sample do not have coulrophobia can be calculated as follows:

( P(\text{none have coulrophobia}) = (0.88)^{10} ).

Calculating ( (0.88)^{10} ):

• ( 0.88^{10} \approx 0.5132 ).

Now, to find the probability that at least one person has coulrophobia, we take the complement of that probability:

( P(\text{at least one has coulrophobia}) = 1 - P(\text{none have coulrophobia}) ).

This gives us:

( P(\text{at least one has coulrophobia}) = 1 - 0.5132 \approx 0.4868 ).

However, looking