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 0.2 0.05 0.25

Loss 0.6 0.15 0.75

Total 0.8 0.20 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. Answer:

Answer 1

Both a and b are independent (see explanation)

Explanation:

Events A and B are independent when

`P(A\cap B)=P(A)\cdot P(B)`

a) A - "winning"

B - "playing at home"

From the table,

`P(A)=0.25\\ \\P(B)=0.8\\ \\P(A\cap B)=0.2`

Since

`0.25\cdot 0.8=0.2`

events are independent.

b) A - "losing"

B - "playing away"

From the table,

`P(A)=0.75\\ \\P(B)=0.2\\ \\P(A\cap B)=0.15`

Since

`0.75\cdot 0.2=0.15`

events are independent.