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lozanna [386]
3 years ago
9

Suppose that in a certain population of married couples, 30% of the husbands smoke, 20% of the wives smoke, and in 8% of the cou

ples 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?
Mathematics
1 answer:
xxTIMURxx [149]3 years ago
6 0

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 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.

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