1. ## Probabilty with events

We did this ages ago and I really can't remember how to do it! You will be loved forever if you can help me with this!

Question

The events A and B are such that

P(A) = 5/16, P(B) = 1/2 and P(A|B) =1/4

Find
(a) P(AnB)
(b) P(B'|A)
(c) P(A'uB)
(d) Determine, with reason, whether or not the events A and B are independant.

I know it's probably the easiest thing ever but I really can't remember what to do

2. Originally Posted by jonannekeke
We did this ages ago and I really can't remember how to do it! You will be loved forever if you can help me with this!

Question

The events A and B are such that

P(A) = 5/16, P(B) = 1/2 and P(A|B) =1/4

Find
(a) P(AnB)
(b) P(B'|A)
(c) P(A'uB)
(d) Determine, with reason, whether or not the events A and B are independant.

I know it's probably the easiest thing ever but I really can't remember what to do

Do you know the definition for conditional probability?

$\displaystyle P(A|B)=\frac{P(A\cap B)}{P(B)}$

or using the notation you used

P(A|B)=P(AnB)/P(B)

provided P(B)>0

(Hopefully this site will get latex back soon)

3. I'm sorry, I don't understand I don't know why but I really can't remember any of this probability stuff, how do you actually work out P(AnB)? I'm so confused

4. P(A|B)=P(AnB)/P(B)

using the above in the form

P(AnB) =P(A|B)P(B)

=1/4*1/2=1/8

---------

P(B'|A)=1-P(B|A)

=1-P(BnA)/P(A)=1-P(A|B)*P(B)/P(A)

=1-1/4*(1/2)/(5/16)
=1-1/4*1/2*(16/5)
=1-2/5=3/5

---------

Can you figure out the rest?

5. I'm not sure

Has part (c) got something to do with 1- P(A) or am I completely wrong?

6. P(A'uB)=1-P(AnB')

=1-P(B'|A)*P(A)

=...

7. ... so would that be

1-(3/5)*(5/16)?

8. Originally Posted by jonannekeke
... so would that be

1-(3/5)*(5/16)?
yes

9. Yay at least I did one bit, kinda

I don't get part (d) though...

10. Originally Posted by jonannekeke
Yay at least I did one bit, kinda

I don't get part (d) though...
Two events are independent if knowing that one occurs tells you nothing about whether the other occurs.