Q:

Suppose that in a certain population of married couples, 30% of the husbands smoke, 20% of the wives smoke, and in 8% of the couples both the husband and the wife smoke. Is the smoking status (smoker or non-smoker) of the husband independent of that of the wife? Why or why not?

Accepted Solution

A:
Answer:Not independent Step-by-step explanation:Given that in a certain population of married couples, 30% of the husbands smoke, 20% of the wives smoke, and in 8% of the couples both the husband and the wife smoke. Let A be the event that husbands smoke and B the event that wives smokeGive that[tex]P(A) = 0.30\\P(B) = 0.20\\P(A\bigcap B) = 0.08[/tex]To check whether A and B are independent it is sufficient to checkP(A\bigcap B)=P(A)P(B)Right side=[tex]P(A)P(B)\\=0.3(0.2)\\=0.06[/tex]Left side = 0.08Since two sides do not equal the two events are not independent.