Statistics Homework Help!

Question

The table shows the percentages of residents in a large community when classified according to gender and presence of a particular allergy: 

 

Allergy:  Male Present 16, Male Absent 36,  Female present 9, Female absent 39

 

Suppose that the selection of a person is considered a trial, and the [presence of an allergy is considered a success. For each case identify the numerical value of p and the the probability.

 

A)  Four persons are selected at random.  What is the probability that none has the allergy?

 

B)  Four males are selected at random.  What is the probability that none has the allergy?

 

C)  Two males and two females are selected at random.  What is the probability none has the allergy? 

Answer 1

Hello Jeff,

 

The sample size of the "large community" seems small, at only 100 people.

 

For A, first calculate the probability that your first pick is allergy free: P(no allergy on 1st pick) = 75/100, since there are 75 without the allergy out of 100 people.

 

Multiply by 4 picks. You can approximate this as (3/4)4, which is 0.32. Or calculate it exactly, accounting for people already picked and the diminishing sample size:

 

P(no allergy in 4 picks) = (3/4)(74/99)(73/98)(72/97) = 0.31.

 

Does this pass the "sniff test?" That is, does it seem reasonable that, in a population where 1/4 of the people have the allergy, your chances of getting 4 picks in a row of no allergy are only about 0.3?

 

Yes.

 

B. Calculate this one the same, but use 52 as your original population size: P = (36/52)(35/51)(34/50)(34/49).

 

C. Calculate the two probabilities separately. P(two men with no allergy) = (36/52)(35/51). P(two women without allergy) = (30/39)(29/38). Then multiply these probabilities together. This last one is made straightforward because the sample populations are mutually exclusive.

 

Stay away from the peanuts and shellfish.

 

 

Eric M.

McMinnville OR