Question

10. Is the probability that a randomly selected student who has asthma and who has a household member who smokes the same as or different from the probability that a randomly

selected student who does not have asthma but does have a household member who smokes? Explain your answer.

Answer 1

No probabilities are not equal.

Probability of a randomly selected student who has asthma and who has a household member who smokes = 0.62

probability of a randomly selected student who does not have asthma but does have a household member who smokes = 0.37

Explanation:

As table in question is not given, so considering the table attached below.

Total no of students having asthma = 182

Total no of students not having asthma = 755

Total no students = 937

No. of students who have asthma and no household member smoke = 69

No. of students who have asthma and no household member smoke = 113

No. of students who have asthma and no household member smoke = 473

No. of students who have asthma and no household member smoke = 282

Probability of a randomly selected student who has asthma and who has a household member who smokes :

`P(S|A) = (P(S \cap A))/(P(A))\\\\=(113)/(182)\\\\=0.62`

Probability of a randomly selected student who does not have asthma but does have a household member who smokes

`P(S|\bar{A})=\frac{P(S\cap \bar{A)}}{P\bar{A}}\\\\=(282)/(755)\\\\=0.37`