Question

Are the events “winning” and “playing at home” independent? Explain why or why not.Are the events “losing” and “playing away” independent? Explain why or why not.Answer:

Answer 1

a) In general, if two events, A and B, are independent,

`\begin{gathered} A,B\rightarrow\text{ independent events} \\ \Rightarrow P(A\cap B)=P(A)*P(B) \end{gathered}`

Therefore, in our case,

`\begin{gathered} P(Winning\cap Home)=0.2 \\ and \\ P(Winning)*P(Home)=0.25*0.8=0.2 \end{gathered}`

Thus, the two events are independent.

b) Similarly,

`\begin{gathered} P(losing\cap away)=0.15 \\ and \\ P(losing)P(away)=0.75*0.20=0.15 \end{gathered}`

The two events are independent.

Furthermore, the intersection of two independent events is different than the empty set.