# Conditional probabilty; dependent and independent events

• Oct 6th 2010, 08:10 AM
jlt199
Conditional probabilty; dependent and independent events
This is my first post to this forum. I feel it's time I gained a proper grasp on probabilty and statistics, so I've started working my way through a text book on the subject... I made it as far as page 7!

P(B|A) is the probabilty of B given that A is true. I understand that to mean that the event occuring in A is certain (P(A) = 1), given that, what is the probabilty of the event also occurring in B. ie. the sample space is now A, what is the probabilty of the event being in the region A$\displaystyle \cap$B?

So, independent events; I take this to mean both occur in the same sample space, but there is no overlap between them. Is that correct?

I don't understand why P(B|A) = P(B), by my thinking it should be zero!

If anyone can understand my ramblings and help me understand what I am missing I would be grateful.

Many thanks
• Oct 6th 2010, 08:39 AM
harish21
$\displaystyle P(B|A) = \frac{P(B \cap A)}{P(A)}$

if two events are independent, then $\displaystyle P(B \cap A) = P(B) \times P(A)$

Also,

$\displaystyle P(B \cap A) = 0$ if the events are MUTUALLY EXCLUSIVE

and Mutually Exclusive and Independent do NOT mean the same
• Oct 6th 2010, 08:53 AM
jlt199

So, P(B|A) = 0 if the events are mutually exclusive.

How then would you explain what independent events are to a three year old? (I feel that is about my mental age these days!)

Would is be something like the probabilty of throwing a six with a die and drawing a king from a deck of cards? ie. $\displaystyle P(6\cap K) = 1/6 \times 1/13$

Would independent events have completely seperate sample spaces when considering a Venn (?) diagram?
• Oct 6th 2010, 09:00 AM
harish21
events A and B are independent if the probability that A occurs does not affect the probability of B occuring.

Yes, the example you have mentioned works.
• Oct 6th 2010, 09:10 AM
jlt199
Ok, I think I've got it now. Thanks for your help

...onto the next section!