Question

The table shows the probabilities of winning or losing when the team is playing away or is playing at home.

(a) Are the events “winning” and “playing at home” independent? Explain why or why not.
(b) Are the events “losing” and “playing away” independent? Explain why or why not.

Answer 1

Although the experimental probability shows that playing at home gives a certain edge, mathematically the events "winning" and playing at home are completely independent since the 2 events are not linked whatsoever.
Just take the example of flipping a dye. The probability of getting a Head = 1/2.
If after 1000 flips you get a head, the probability of getting a Head on the 1001 flips is always 1/2 (head & tail are independent)

Same reasoning for the 2nd question

Answer 2

Based on the given data on winning and losing at home or away from home, we can conclude that:

(a) The events “winning” and “playing at home” are not independent of each other. This is because the probability of winning at home is not equal to the probability of winning away from home. (0.2 > 0.05)

(b) The events “losing” and “playing away” are not independent of each other. This is again because the probability of losing at home is not equal to the probability of losing away from home. (0.6 > 0.1)