Question

Food allergies affect an estimated 7% of children under age 5 in the US. What is the probability that in a kindergarden class of 12 kids under age 5 at least one of them has food allergies? You may assume that the students in this class are a representative random sample from the population.

Answer 1

5=7%=7/100

Explanation:

Answer 2

Probability of atleast one of 12 student has food allergies ≈ 0.58 ( approx)

Explanation:

Given: Probability of a children under age 5 has food allergies = 7%

=
`(7)/(100)`

To find : Probability of atleast one of 12 student has food allergies

Probability of a chindren under age 5 does not have food allergies =
`1-(7)/(100)`

⇒ prob =
`(93)/(100)`

now we find Probability of atleast one of 12 student has food allergies this means we have to find prob of 1 student, 2 student, 3 student, till 12 student have allergy out of 12 student of class then add all prob.

But instead of finding all these probability we find probability of student having no allergy.i.e., 0 student then subtract it from 1(total probability)

Probability of 0 student having allergy out of 12 student =
`((93)/(100))^(12)`

Therefore, Probability of atleast one of 12 student has food allergies

=
`1-((93)/(100))^(12)`

=
`0.581403702521`

≈ 0.58 ( approx)