5. In Somewhere City USA, 72% of its adult residents viewed the SuperBowl last y

Question

5. In Somewhere City USA, 72% of its adult residents viewed the SuperBowl last year.  The town demographics showed that it contained 48% adult males in the city.  The proportion of residents that can be categorized as either adult male or an adult that viewed the SuperBowl is 80.16%. To answer the questions below assume that the town is a perpetual locked box: no new residents move in, no one dies, etc.

When answering probability questions, write each question in function notation.

a. What is the probability that a person chosen at random is an adult woman and she also watched the SuperBowl last year?

b. What is the probability that a person chosen at random is not an adult man and also did not watch the SuperBowl last year.

c. Are the events an adult male, adult viewed the SuperBowl independent events? A yes or no answer alone will not receive any credit. You must show proof for your yes or no response.

Explanation / Answer

Let say Superbowl viewer is event A and adult male is event B

Pr(superbowl viewer) = P(A) = 0.72

P(not superbowl viewer) = P(A') = 0.28

Pr(adult males) = P(B) = 0.48

P(adult females) = P(B') = 0.52

Pr(Adult male or adult that viewed superbowl) = P(A U B) = 0.8016

P(A U B) = P(A) + P(B) - P(A B)

0.8016 = 0.72 + 0.48 - P(A B)

P(A B) = 0.3984

(a) Here we have to find that a person chosen is adult women and she watched the superbowl.

Pr(Adult women and super bowl viewer = P (A' B) = P(Superbowl viewer) - P(Adult men and superbowl viewer) = 0.72 - 0.3984 =  0.3216

(b) Pr(Not a adult man and also didnot watch superbowl last year) = Pr(A' B') = 1 - P(A U B) = 1 - 0.8016 = 0.1984

(c) Here we have to find that if A and B are independent events or not.

They wil be independent events if

P(A B) = P(A)P(B) or P(A lB) = P(A)

so  P(A B) = 0. 3984

P(A)P(B) = 0.72 * 0.48 = 0.3456

so no thesse two events are not independent.

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