Question

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?

Answer 1

Not independent

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 smoke

Give that

`P(A) = 0.30\\P(B) = 0.20\\P(A\bigcap B) = 0.08`

To check whether A and B are independent it is sufficient to check

P(A\bigcap B)=P(A)P(B)

Right side=
`P(A)P(B)\\=0.3(0.2)\\=0.06`

Left side = 0.08

Since two sides do not equal the two events are not independent.