Question

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

home. away. total
Win: 056. 0.24. 0.8
Loss: 0.14. 0.06. 0.2
Total: 0.7. 0.3. 1.00

a) are the events 'winning' and 'playing at home' independent? show your calculations to justify why or why not.
b) Are the events "losing" and "playing away" independent? show your calculations to justify why or why not.​

Answer 1

• Use numbers from respective cells of the table for calculations

a) Are the events 'winning' and 'playing at home' independent?

• p(winning and playing at home) = 0.56
• p(winning)*p(playing at home) = 0.8*0.7 = 0.56

Since the probabilities are same, the events are independent

b) Are the events "losing" and "playing away" independent?

• p(losing and playing away) = 0.06
• p(losing)*p(playing away) = 0.2*0.3 = 0.06

Since the probabilities are same, the events are independent