IfCandDare events such that Pr(C) = 0.6 , Pr(D) = 0.5 andCandDare independent, find

aPr(C|D)

bPr(C U D)

I am unsure how to start, as I don't know what the symbols represent and what is needed?

Any help would be greatly appreciated!

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- Aug 22nd 2009, 01:11 AMscubasteve94Probability
If

*C*and*D*are events such that Pr(C) = 0.6 , Pr(D) = 0.5 and*C*and*D*are independent, find

**a**Pr(C|D)

**b**Pr(C U D)

I am unsure how to start, as I don't know what the symbols represent and what is needed?

Any help would be greatly appreciated! - Aug 22nd 2009, 01:36 AMCaptainBlack
Pr(X) denotes the probability of X

Pr(X|Y) denotes the probability that X occurs given that Y occurs

Pr(X U Y) denotes the probability of the union of events X and Y, that is the probability that one or other or both occur.

If C and D are independednt Pr(C and D)=Pr(C)Pr(D) - this is the definition of independednce.

Also: Pr(C and D)=Pr(C|D)Pr(D).

That should be sufficient to do part (a)

For part (b) you need:

Pr(C U D)=Pr(C)+Pr(D)-Pr(C and D)

CB - Aug 25th 2009, 11:36 PMmatheagle
equivalent definitions to independence are

P(C|D)=P(C)

P(D|C)=P(D)

and

P(CD)=P(C)P(D)

Any of these implies the other two

and of course if one holds, all three hold

and if one fails the other two fail

The first two are the natural definition of independence

The chance of C happening is the same no matter if D occurs or not.