1. ## find probability

I have a probability problem where probability of neither A nor B is 35%. 30% is A and 40% is B. How do i find the probability of both A and B?

Also, where can i review how to do probability and stats like this?
Please dont leave the answer.. I need to try to figure this out, thanks!

2. Originally Posted by cowgirl123
I have a probability problem where probability of neither A nor B is 35%. 30% is A and 40% is B. How do i find the probability of both A and B?

Also, where can i review how to do probability and stats like this?
Please dont leave the answer.. I need to try to figure this out, thanks!
Hint: $P(\overline{A} \cap \overline{B}) = P(\overline{A \cup B}) = 1 - P(A \cup B)$

3. Is the answer .12? Or is this wrong?

4. Originally Posted by cowgirl123
Is the answer .12? Or is this wrong?
Its wrong... Show us your work and we will tell your mistake. I can give you the solution but it may not help you a lot. I will give you a new hint.

Hint:

$P(\overline{A} \cap \overline{B}) = 1 - P(A \cup B) = 1 - (P(A) + P(B) - P(A \cap B))$

5. Originally Posted by Isomorphism
Its wrong... Show us your work and we will tell your mistake. I can give you the solution but it may not help you a lot. I will give you a new hint.

Hint:

$P(\overline{A} \cap \overline{B}) = 1 - P(A \cup B) = 1 - (P(A) + P(B) - P(A \cap B))$
I think my problem is not knowing what exactly to do with the unions and intersections. I thought the intersection sign meant to multiply the numbers.. But i dont think this is right. Bc i end up with

$1 - P(A \cup B) = 1 - (.3 + .4 - (.3 * .4)) = 1 - (.7 - .12) = 1 - .58 = .42$

6. Originally Posted by cowgirl123
I think my problem is not knowing what exactly to do with the unions and intersections. I thought the intersection sign meant to multiply the numbers.. But i dont think this is right. Bc i end up with

$1 - P(A \cup B) = 1 - (.3 + .4 - (.3 * .4)) = 1 - (.7 - .12) = 1 - .58 = .42$
What you are thinking is wrong generally. Only for the specific case of A and B being independent events, we can multiply probabilities...

"probability of neither A nor B is 35%" $\Rightarrow P(\overline{A} \cap \overline{B})$
We want the "probability of both A and B" $\Rightarrow P(A \cap B)$

$P(\overline{A} \cap \overline{B}) = 1 - (P(A) + P(B) - P(A \cap B)) \Rightarrow P(A \cap B) = P(\overline{A} \cap \overline{B}) + P(A) + P(B) - 1$

$P(A \cap B) = P(\overline{A} \cap \overline{B}) + P(A) + P(B) - 1 \Rightarrow P(A \cap B) = 0.35 + 0.3 + 0.4 - 1 = 0.05$

7. .05?
Could you give me the list of...rules.. for things like this? I have a lot to learn.. and i cant find a set of things to do for certain problems.

$.35 + .3 + .4 - 1 = .35 + .7 - 1 = 1.05 - 1 = .05$

8. Originally Posted by cowgirl123
.05?
Could you give me the list of...rules.. for things like this? I have a lot to learn.. and i cant find a set of things to do for certain problems.

$.35 + .3 + .4 - 1 = .35 + .7 - 1 = 1.05 - 1 = .05$
Dont you have a text book? I can suggest a plan though... First learn basic set theory. Intersection, Compliments, DeMorgans Laws, Unions, Venn Diagrams etc. Then try learning probability

9. Originally Posted by cowgirl123
I have a probability problem where probability of neither A nor B is 35%. 30% is A and 40% is B. How do i find the probability of both A and B?

Also, where can i review how to do probability and stats like this?
Please dont leave the answer.. I need to try to figure this out, thanks!
I'd suggest drawing a Karnaugh Table:

$\, \begin{tabular}{l | c | c | c} & A & A\, ' & \\ \hline B & & & 0.4 \\ \hline B\, ' & & 0.35 & \\ \hline & 0.3 & & 1 \\ \end{tabular}
$

Fill in the blank cells (just like a sudoko puzzle). Then add up the probabilities in the cells that relate to your question.

10. Originally Posted by mr fantastic
I'd suggest drawing a Karnaugh Table:

$\, \begin{tabular}{l | c | c | c} & A & A\, ' & \\ \hline B & & & 0.4 \\ \hline B\, ' & & 0.35 & \\ \hline & 0.3 & & 1 \\ \end{tabular}
$

Fill in the blank cells (just like a sudoko puzzle). Then add up the probabilities in the cells that relate to your question.
I've never done sudoko.. are the columns and rows supposed to add up to the same number? And do you just have to start guessing numbers until it works?

11. Originally Posted by cowgirl123
I've never done sudoko.. are the columns and rows supposed to add up to the same number? And do you just have to start guessing numbers until it works?