A markeling company has randomly surveyed 196 men wha watch

A markeling company has randomly surveyed 196 men wha watch professional sparts. The men were separated according to their educational level (college degree ar not) and whether they preferred the NEA or the National Foll Sports League (NFL). The results of the survey are shavwn to the right Camplele parts a through d ollege No College\' Preference NDA NFL a. What is the probability that a randomly selected survey participant prefers the NFL? Round to four decimal places as needed.) b. What is he probability that a randomly selected survey partcipant has a college degree and prefers the NBA? Round to four decimal places as needed.) c. Suppose a survey participant is randomly selected and you are told that he has a colege degree. What is the probability that this man prefers the NFL? (Round to four dacimal places as needed) d Is a survey participant\'s preference for tha NBA independent of having a college degree? O Yes. Tha two avents are indapandent O No. The two avents are not independent

Solution

(a)

Total number of participants = 195

Total number of participants who watch NFL = college degree + no college degree

= 13 + 93 = 106.

Let A be the event that a randomly selected participant watches NFL

P(A) = Total number of participants who watch NFL / Total number of men who watch professional sports.

= 106 / 195

= 0.543589 = 0.5436

(b)

Total no. of participants who have a college degree and prefer NBA is 36.

Let A be the no. of participants have college degree and prefers NBA

P(A) = Total number of college degree participants / total no of men who watch sports

= 36 / 195

= 0.1846153 = 0.1846

(c)

Total no. of participants who have college degree = 49

Let A be the randomly selected men from NFL

P(A) = Total men who have college degree / men from NFL

= 13 / 49

= 0.26530

(d)

let (A) be the men prefers NBA

B be the men has college degree

A AND B will be independent if

P( A and B) = P(A).P(B).........(1)

P (A,B) = 36 / 195

= 0.18461

P(A) = 93 / 195

= 0.4769

P(B) = 49 / 196 = 0.2512

So, P(A,B) NOT EQUAL P(A).P(B) So, A and B are not independent

No, the two event are not independent.