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%
=[tex]\frac{7}{100}[/tex]
To find : Probability of atleast one of 12 student has food allergies
Probability of a chindren under age 5 does not have food allergies = [tex]1-\frac{7}{100}[/tex]
⇒ prob = [tex]\frac{93}{100}[/tex]
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 = [tex](\frac{93}{100})^{12}[/tex]
Therefore, Probability of atleast one of 12 student has food allergies
= [tex]1-(\frac{93}{100})^{12}[/tex]
= [tex]0.581403702521[/tex]
≈ 0.58 ( approx)
