Answer:
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
Step-by-step 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 :
[tex]P(S|A) = \frac{P(S \cap A)}{P(A)}\\\\=\frac{113}{182}\\\\=0.62[/tex]
Probability of a randomly selected student who does not have asthma but does have a household member who smokes
[tex]P(S|\bar{A})=\frac{P(S\cap \bar{A)}}{P\bar{A}}\\\\=\frac{282}{755}\\\\=0.37[/tex]
