Probability Help

[Flaming_Arrow]

when do i know if i have to use Intersection(n) or Given(|). also whats the difference between them?

The current football fixture has the local team playing at home 60% of its matches. when it plays at home, the team wins 80% of the time. when it plays away, the team wins only 40% of the time. what % of its games does the team play away and win?

would i use given or intersection in this case?


Thanks

[chid]

I am not sure whether you actually need to use intersection or given. Given implies conditional probability and so you divide the intersection by the condition.
Pr(A given B)= Pr(A intersection B)/Pr(B)

I would use a tree diagram:

Pr(home)=0.6 and Pr(away)=0.4

From the 'home branch' Pr(win)=0.8 Pr(loss)=0.2 and from the 'away branch' Pr(win)=0.4 and Pr(loss)=0.6

Therefore, Pr( play away and win)=0.4x0.4=0.16 (16%)

I hope this is correct... let me know either way

[/0]

The expression is the probability of A happening given that you already know B happens. If you had to apply that to this question, the question would have to read: "What % of its games does the team win given that it plays away" (incidentally, the question already gives you this as 0.4).

But in this case what you need is , not

From the information given,





And since







Edit: beaten by chid

[Flaming_Arrow]

oh i think i get it now
thanks guys