Can someone help me with this, I'm a tad bit confused.

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)

are you super sure about this because this a very important test and I am very lost on this question

I'm seeing that 

P[win at home] = 0.2 = 0.8 x 0.25 = P[win] x P[at home]

therefore the two are independent.

test?

You are asking us to give you the answer for a test you are taking?

Is your teacher/proctor aware of this?

Im just going to stop right here

Not a test but a quiz. I've answered all the other questions I just can't figure this out. 

.......

I have lost the thread of this conversation 

We should get some flowers for Rom, too.  

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You didn’t lose the thread, Nicolas; you never had it in the first place.