Question

We are interested in analyzing data related to football players for one season. Use T to denote the player is in their 30s and use F to denote a player plays offense. The probability that someone in their 30s in the data set is 10.2%. The probability that someone plays offense in the data set is 48.6%. The probability that someone is in their 30s and plays offense if 4.9%. What percentage of people in the NFL are in their 30s or play offense? What percentage of people in the NFL are in their 30s and do NOT play offense? Given someone is in their 30s, what is the probability that they play offense? What percentage of players are NOT in their 30s and are NOT on offense? Are T and F mutually exclusive events? Why or why not? Are T and F independent events? Explain, using probabilities. If we know someone plays offense, what is the probability they are in their 30s?

Answer 1

Answer:1.)49%

2.)5.3%

3)4.9%

4)46.1%

5)the events are independent of each other but not mutually exclusive.

6)4.9%

Explanation:

From the data given

Event that a player in Npfl plays in his 30s is T

Event that a player plays in offense position is F

Drawing a set diagram

P(T) =10.2%

P(F)=48.6%

P(TnF)=4.9%

1.probability of T only or F only=10.2-4.9+48.6-4.9=49%

2.prob(Tonly)=prob(T)-Prob(PnT)

=10.2-4.9=5.3%

3.prob(TnF)=4.9%

4.Pr(TUF)'=100-{pr(Tonly)+Pr(Fonly)+P(TnF)}

100-(10.2-4.9+48.6-4.9+4.9)

100-(5.3+43.7+4.9)

=46 .1%

D.the two events are independent of each other i.e the occurrence of being in 30s and being an offensive players can happen simultaneously.

For thatsame reason ,they are NoT mutually exclusive.

E) prob (playing in 30s and being offensive) is p(TnF)=4.9%