# statistics and probability question

#### rsniper007

##### New Member
Winnipeg has three professional sports teams - the Winnipeg Jets hockey team, the Winnipeg Blue Bombers football team and the Winnipeg Goldeyes baseball team.

Suppose we have the following information about Winnipeg residents:

55% are Jets fans (J)
40% are Bombers fans (B)
64% are Jets fans or Goldeyes fans (G)
50% are Bombers fans or Goldeyes fans
27% are Jets fans and Bombers fans
11% are Jets fans and Goldeyes fans
6% are fans of all three teams

We will randomly select one Winnipeg resident.

(a) The outcome of interest is which (if any) of the three teams the person is a fan. List the complete sample space of outcomes.

(b) What is the probability that the selected person is a Jets fan or a Bombers fan?

(c) What is the probability that the selected person is a Goldeyes fan?

(d) What is the probability that the selected person is a Bombers fan and a Goldeyes fan?

(e) Are any two of the events (J, B, G) independent of one another? Explain.

(f) Are any of the two events (J, B, G) mutually exclusive of one another? Explain.

(g) Without doing any calculations, what is the probability that a Goldeyes fan is also a Jets fan?

(h) What is the probability that the selected person is a Jets fan but not a Bombers fan?

(i) What is the probaiblity that the selected person is a Jets fan if we know they are not a Bombers fan?

(j) What is the probaiblity that the selected person is a Goldeyes fan if we know they are a fan of the Jets and Bombers?

(k) What is the probability that the selected person isn't a fan of any of the three teams?