Question

1. We are interested in analyzing data related to college football. Use S to denote the team is in the SEC and use W to denote a team has a winning season. The probability that a team is in the SEC in the data set is 5.5%. The probability that a team has a winning season is 52.5%. The probability that a team is in the SEC and has a winning season is 3.55%.

2. 1. What percentage of teams are in the SEC or had a winning season?

   2. What percentage of people teams are in the SEC and did NOT have a winning season?

   3. Given a team had a winning season, what is the probability that they are in the SEC?

   4. What percentage of players are NOT in the SEC and did NOT have a winning season?

   5. Are S and W mutually exclusive events? Why or why not?

   6. Are S and W independent events? Explain, using probabilities.

   7. If we know a team is in the SEC, what is the probability that they had a winning season?

Answer 1

from given data:

	S	S'	total
W	0.0355	0.4895	0.525
W'	0.0195	0.4555	0.475
total	0.055	0.945	1

a)

percentage of teams are in the SEC or had a winning season=P(S or W) =P(S)+P(W)-P(S n W) =5.5+52.5-3.55=54.45 %

b)

percentage of people teams are in the SEC and did NOT have a winning season

=P(S)-P(S n W) =5.5-3.55 =1.95 %

c)

P(S |W )=P(S n W)/P(W) =3.55/52.5 =0.0676

d)

percentage of players are NOT in the SEC and did NOT have a winning season

=100-P(S or W) =100-54.45 =45.55 %

e)
S and W are not mutually exclusive since P(S and W) is not equal to 0

f)

since P(S)*P(W) is not equal to P(S n W) ; therefore S and W are not independent events.

g)

P(W |S)=P(S n W)/P(S) =3.55/5.5 =0.6455