# 3 Stats problems... need help

• Sep 24th 2007, 08:26 AM
statsaway
3 Stats problems... need help
Hello,

This is my first post here. I'm in need of some help understanding these three problems.

#1. Determine all joint probabilities from the following.

P(A)= .8
P(BlA)= .4
P(Ac)= .2
P(BlAc)=.7

read the letter c as complement.

From this I figure I need to find the following probabilities:

P(A and B), P(A and Bc), P(Ac and B), and P(Ac and B). The c's should be read as complement.

So, how do I do this? I'm kind of confused at this point. I'm sure I have to draw a table.. but I'm not sure how.. please, if you can.. help me.

#2. Given the following probabilities, draw a probability tree to compute the joint probabilities.

P(A)= .8
P(BlA)= .3
P(Ac)= .2
P(BlAc)=.3

Again..I feel that I need to find the probabilities of the following for the tree:

P(A and B), P(A and Bc), P(Ac and B), and P(Ac and B). The c's should be read as complement.

#3. I'll get to this later. I would like some help with the first two problems. I"m not sure were to go with those. Thanks!
• Sep 24th 2007, 11:03 AM
statsaway
Hello,

I'm sitting here confused. I made up a chart.. but I'm almost certain it is not correct. However, I'm thinking now that I do not have to make a chart for this problem.

Problem #1. The joint probability for P(A) = .8 given the rest of the Probabilities in that problem is .32 since P(A)*P(BofA)=.32? Not sure.. but I think I'm right about that one.

Wouldn't the probability of P(BofA)=.32 also since it is also using the multiplication rule?

I'm not sure what to do with the complements.

Thanks!
• Sep 24th 2007, 12:31 PM
Plato
What does P(BofA) mean?
I have never seen that notation.
• Sep 24th 2007, 12:37 PM
Jhevon
Quote:

Originally Posted by statsaway
Hello,

This is my first post here. I'm in need of some help understanding these three problems.

#1. Determine all joint probabilities from the following.

P(A)= .8
P(BlA)= .4
P(Ac)= .2
P(BlAc)=.7

read the letter c as complement.

From this I figure I need to find the following probabilities:

P(A and B), P(A and Bc), P(Ac and B), and P(Ac and B). The c's should be read as complement.

So, how do I do this? I'm kind of confused at this point. I'm sure I have to draw a table.. but I'm not sure how.. please, if you can.. help me.

#2. Given the following probabilities, draw a probability tree to compute the joint probabilities.

P(A)= .8
P(BlA)= .3
P(Ac)= .2
P(BlAc)=.3

Again..I feel that I need to find the probabilities of the following for the tree:

P(A and B), P(A and Bc), P(Ac and B), and P(Ac and B). The c's should be read as complement.

use the formula for conditional probability.

Recall, that if $P(F)>0$, we have:

$P(E|F) = \frac {P(E \cap F)}{P(F)}$

so, for instance, to find $P(A \cap B)$:

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

$\Rightarrow P(A \cap B) = P(B|A) \cdot P(A)$

and just plug in the values you were given
• Sep 24th 2007, 12:59 PM
statsaway
Quote:

Originally Posted by Plato
What does P(BofA) mean?
I have never seen that notation.

I can't figure out how to type in some math notations. So, I meant it to look like this:

P(BlA) It's a straight up and down line.. I used an Lowercase L instead .. and of instead of the line also.... sorry about the confusion.

Thanks
• Sep 24th 2007, 01:04 PM
statsaway
Quote:

Originally Posted by Jhevon
use the formula for conditional probability.

Recall, that if $P(F)>0$, we have:

$P(E|F) = \frac {P(E \cap F)}{P(F)}$

so, for instance, to find $P(A \cap B)$:

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

$\Rightarrow P(A \cap B) = P(B|A) \cdot P(A)$

and just plug in the values you were given

Hmm.. we have not learned conditional probability formula yet. So, I can't necessarily use that to formulate my answers.

I'll tell you what I have to go by. In this section we learned about the Complement rule, Multiplication rule, multiplication rule for independent events, Addition rule, Addition rule for Mutuallly Exclusive Events.

Before that we learned Intersection of points, conditional probability, independent events, Union of Events A and B.

thanks for your reply.. I really appreciate that.. I will use it in the future.. i'm sure.. but I would like to know how to solve these problems w/o that. This is just basic statistics.. and we are only on chapter 6, just now learning about probability.

Thanks!
• Sep 24th 2007, 01:17 PM
statsaway
Ok, assuming I'm using that conditional prob. formula above.. I'm still looking for Joint probabilities. I already know P(BlA)= .4.. that is given along with P(A)= .5

thanks
• Sep 24th 2007, 01:43 PM
Plato
$P(B^c |A) = 1 - P(B|A)$
• Sep 24th 2007, 06:00 PM
statsaway
Quote:

Originally Posted by Plato
$P(B^c |A) = 1 - P(B|A)$