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!
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!
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
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.