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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 :(
Thanks in advance!
Do you know the definition for conditional probability?Quote:
Originally Posted by jonannekeke
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)
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
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?
I'm not sure
Has part (c) got something to do with 1- P(A) or am I completely wrong?
P(A'uB)=1-P(AnB')
=1-P(B'|A)*P(A)
=...
... so would that be
1-(3/5)*(5/16)?
yesQuote:
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.Quote:
Originally Posted by jonannekeke
for your problem
P(A) = 5/16 and P(A|B) =1/4
if A and B were independent then P(A|B)=P(A)
since they are different the two events are not independent
Thank you sooooo much! :D