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

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Home Away Total

Win 0.2 0.05 0.25

Loss 0.6 0.15 0.75

Total 0.8 0.20 1.00

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(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:

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frika

Answer:

Both a and b are independent (see explanation)

Step-by-step explanation:

Events A and B are independent when

[tex]P(A\cap B)=P(A)\cdot P(B)[/tex]

a) A - "winning"

B - "playing at home"

From the table,

[tex]P(A)=0.25\\ \\P(B)=0.8\\ \\P(A\cap B)=0.2[/tex]

Since

[tex]0.25\cdot 0.8=0.2[/tex]

events are independent.

b) A - "losing"

B - "playing away"

From the table,

[tex]P(A)=0.75\\ \\P(B)=0.2\\ \\P(A\cap B)=0.15[/tex]

Since

[tex]0.75\cdot 0.2=0.15[/tex]

events are independent.

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