(16) 4. In the State of Wisconsin, 20% ofresidents purchase fishing licenses. Fo

Question

(16) 4. In the State of Wisconsin, 20% ofresidents purchase fishing licenses. For the residents who do purchase a fishing license in a year, 40% purchase a hunting license in the same year. For the residents who do not purchase a fishing license in year, only 3% purchase a hunting license in the same year a. What is the probability that a Wisconsin resident purchases a fishing license and b. Are "purchase a fishing license" and "purchase a hunting license" independent c. What is the probability of "purchase a fishing license" or "purchase a hunting d. What is the overall probability of a Wisconsin resident purchasing a hunting a hunting license in a given year? events? Why or why not? Show it with numbers. license in a given year. license?

Explanation / Answer

Solution- Let us denote the following events-

F- Fishing license is purchased

N - Fishing license is not purchased

H - Hunting license is purchased

P(F) = 0.2 and P(N) = 0.8 P(H|F) = 0.4 and P(H|N) = 0.03

(a) P(F and H) = P(H|F) * P(F)

= 0.4 * 0.2

= 0.08

(b) If F and H would be independent, then P(F) = P(F|H)

Here they are not equal, that means they are not independent.

(c) P(H) = P(F) * P(H|F) + P(N) * P(H|N)

= 0.2 * 0.4 + 0.8 * 0.03

= 0.104

P(F or H) = P(F) + P(H) - P(H and F)

= 0.2 + 0.104 - 0.08

= 0.224

(d) P(H) = 0.104 - overall probability of purchasing hunting license.

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