Randomly select a person from a group of people The probabil

Randomly select a person from a group of people. The probability that he/she has a pollen allergy is 0.3. The probability that he/she has a dust allergy is 0.2. The probabilitly that he/she has a pollen and dust allergy is 0.1.

a.) Find the probability that he/she has none of the two types of allergy.

b.) Find the probability that he/she has either pollen allergy or dust allergy.

c.) Find the probability that he/she has only one of the two types of allergy.

d.) If he/she is found to have pollen allergy, what is the probability that he/she also has a dust allergy?

e.) Are having pollen and having dust allergy independent on each other? Why or why not?

Solution

Given that P(P)=0.3,P(D)=0.2,P(P and D)=0.1

a)P(P and D)^C=1-P(P and D)=1-0.1=0.9

b)P(P or D)=P(P)+P(D)-P(P and D)=0.3+0.2-0.1=0.4

e)P(P)*P(D)=0.3*0.2=0.6 P(P and D)

So,      having pollen and having dust allergy are not independent on each other