About 1% of the American population is allergic to peanuts or tree nuts. Choose

Question

About 1% of the American population is allergic to peanuts or tree nuts.
Choose 5 individuals at random and let the random variable X be the number in this sample who are allergic to peanuts or tree nuts.
The possible values X can take are 0, 1, 2, 3, 4, and 5.
In Exercise 12.13 you made a five-stage tree diagram of the outcomes (allergic or not allergic) for the 5 individuals and used it to find the probability distribution of X.
Continue your work from Exercise 12.13.
What is the conditional probability that exactly 1 of the people will be allergic to peanuts or tree nuts, given that at least 1 of the 5 people suffers from one of these allergies?

A.0.9796 B.0.049 C.0.9510 D.0.021

Explanation / Answer

given atleast 1 of the 5 people suffers from one of these allergies

so the possiblities are 1 of the 5 people suffers from one of these allergies (let us say probability is a)

2 of the 5 people suffers from one of these allergies (let us say probability is b)

3 of the 5 people suffers from one of these allergies (let us say probability is c)

4 of the 5 people suffers from one of these allergies (let us say probability is d)

5 of the 5 people suffers from one of these allergies (let us say probability is e)

so for exactly one will be allergic the answer is = a / (a+b+c+d+e)

using our commonsense we can say that the answer is either A or C since a has highest prob

you can get the values of a b c d e from exercise 12.13 assuming you have done it :p

a = (1/100)*(99/100)*(99/100)*(99/100)*(99/100)*5

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