The committee deciding on the TV commercial purchases is allocating their budget
ID: 2928568 • Letter: T
Question
The committee deciding on the TV commercial purchases is allocating their budget. They decide to advertise during 4 shows, Good Wife, NCIS, Sunday Night NFL and Big Bang Theory. One committee member decides to gather some statistics on the favorite/preferred shows of a group of adults. Each person surveyed indicated their single preferred show. No one was allowed to list more than one show. She finds that 30% of the adults are 18-39 years old, 40% are 40-62 years old and the rest are over 62. Of the oldest adults surveyed, she finds that 36 and 2/3 percent prefer NCIS, 26 and 2/3 percent prefer Sunday Night Football, 21 and 2/3 percent prefer the Big Bang Theory. Of those 40-62, fifteen percent prefer the Good Wife, 25% prefer NCIS, and 45% prefer the Big Bang Theory. Of those 18-39, fifteen percent prefer the Good Wife, 30% prefer NCIS, and twenty percent prefer Sunday Night football. 2.5. What proportion of these adults prefer a show other than Sunday Night Football or are under 40? A. 0.50 B. ~1 C. none of the above D. 0.76 E. 0.94 The committee deciding on the TV commercial purchases is allocating their budget. They decide to advertise during 4 shows, Good Wife, NCIS, Sunday Night NFL and Big Bang Theory. One committee member decides to gather some statistics on the favorite/preferred shows of a group of adults. Each person surveyed indicated their single preferred show. No one was allowed to list more than one show. She finds that 30% of the adults are 18-39 years old, 40% are 40-62 years old and the rest are over 62. Of the oldest adults surveyed, she finds that 36 and 2/3 percent prefer NCIS, 26 and 2/3 percent prefer Sunday Night Football, 21 and 2/3 percent prefer the Big Bang Theory. Of those 40-62, fifteen percent prefer the Good Wife, 25% prefer NCIS, and 45% prefer the Big Bang Theory. Of those 18-39, fifteen percent prefer the Good Wife, 30% prefer NCIS, and twenty percent prefer Sunday Night football.Explanation / Answer
From the given information we have
P(under 40) = P(18-39 years) =0.30
P(Sunday night football) = P(Sunday night football|18-39 years)P(18-39 years)+P(Sunday night football| 40-62 years)P(40-62 years) +P(Sunday night football| over 62)P(Over 62) = 0.20 *(0.30) + 0.15 * 0.40 + (80/(3*100)) *0.30 =0.06+0.06+0.08 =0.2
P(Sunday night football and under 40) = P(Sunday night football|18-39 years)P(18-39 years) = 0.06
So
P(Sunday night football or under 40) = P(Sunday night football) +P(under 40) -P(Sunday night football and under 40) = 0.2+0.3 - 0.06 = 0.44
Correct answer : C