Food allergies affect an estimated 7% of children under age 5 in the US. What is the probability that in a kindergarden class of

Question

2 years ago

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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.

Mathematics

2 answers:

bezimeni [28] · Answer 1 · 2022-09-01T20:02:05+03:00

Answer:

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

Step-by-step explanation:

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

= $\frac{7}{100}$

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

Probability of a chindren under age 5 does not have food allergies = $1-\frac{7}{100}$

⇒ prob = $\frac{93}{100}$

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 = $(\frac{93}{100})^{12}$