Two S1 questions D:

Can someone help me with these please?

The three events A, B and C are defined in the same sample space. The events A and C are
mutually exclusive. The events A and B are independent.

Given that P(A) = 2/5, P(C) = 1/3 or P(A U B ) = 5/8 find


(a) P(A U C),

(b) P(B).

(Do i draw 3 circles?)
The events A and B are independent with P(A) = 1/2 and P(A U B) = 2/3
Find
(a) P(B),

(b) P(A|B),

(c) P(B'|A).

(I don't get this mutually exclusive and Independent stuff )

I am not sure how to help without just giving the answers, but anyway

P(AUC)= probability of BOTH A and C occuring which is 1/3+2/5

We know

P(AUB)=P(A)+P(B) -P(AnB)

but as A and B are independent then P(AnB)=P(A)P(B)

so solving for P(B) we get

5/8= 2/5 + P(B) -p(B)2/5
so P(B)=9/56

For the second question we have:

(a), to find P(B) follow the same process as I have in the previous question, noting A and B are independent.

(b) For conditional probability just use the formula

(c) Do you mean B' is the complement or?

5/8= 2/5 + P(B) -p(B)2/5
so P(B)=9/56 Could you tell me how yo u got this?

By making a mistake

Actually I think all you have to do is just note P(omega)=1 thus 1=P(C) +P(A) +P(B) thought this would give you 4/15. Sorry about that, its too late for me.

So.. whats the right answer?