Joselyn and Tanya are on a swim team. The table below shows the probabilities of the team winning or losing when the team is playing away or is playing at home.

Question

Are the events “winning” and “playing at home” independent?  (5 points)

    Show all of your work proving your statement

	Home	Away	Total
Win	0.6	0.2	0.8
Loss	0.15	0.05	0.2
Total	0.75	0.25	1.00

Answer 1

By looking at the table, we can see that these events will be independent: this team wins 75% of its home games, and also wins 75% of its away games. Thus, the location of the game doesn't bear on the odds of their winning.

We can demonstrate the independence of these events by either of the following calculations:

1) Show "winning" (W) and "playing at home" (H) are independent by showing that P(W and H) = P(W)·P(H)

P(W and H) = .6 (top left cell of table) P(W) = .8 , P(H) = .75 and P(W)·P(H) = .6

OR ...

2) Show P(W|H), probability of "winning" given "team plays at home," is = to P(W).

P(W|H) = P(W and H) / P(H) = .6 / .75 = .8 = P(W)

The above calculation shows that knowing the team is playing at home does not affect its likelihood of winning.