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

Home away Total

Win 0.2 0.05 0.25

Loss 0.6 0.1 0.7

Total 0.8 0.15 1.00

(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.

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