# Probabilty with events

• March 20th 2007, 03:22 PM
jonannekeke
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 :(

• March 20th 2007, 03:58 PM
frenzy
Quote:

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?

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

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)
• March 20th 2007, 04:05 PM
jonannekeke
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
• March 20th 2007, 04:38 PM
frenzy
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?
• March 20th 2007, 04:46 PM
jonannekeke
I'm not sure

Has part (c) got something to do with 1- P(A) or am I completely wrong?
• March 20th 2007, 04:52 PM
frenzy
P(A'uB)=1-P(AnB')

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

=...
• March 20th 2007, 05:00 PM
jonannekeke
... so would that be

1-(3/5)*(5/16)?
• March 20th 2007, 05:02 PM
frenzy
Quote:

Originally Posted by jonannekeke
... so would that be

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

yes
• March 20th 2007, 05:04 PM
jonannekeke
Yay at least I did one bit, kinda :)

I don't get part (d) though...
• March 20th 2007, 05:08 PM
frenzy
Quote:

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.