Basic probability problem: Good Luck!

[Dr. Zaus]

Find a solution to the following:

If you see an Aardvark you have a 65% chance of seeing a Bear. You have an 80% chance of seeing either an Aardvark or a Bear. Aardvarks do not lead to Bears and Bears do not lead to Aardvarks. What are the probabilities of:

seeing an Aardvark AND seeing a Bear
seeing an Aardvark AND not seeing Bear
not seeing an Aardvark AND seeing a Bear

 

[rcpratt]

I feel like this is too simple, therefore I am abstaining to save myself the embarrassment.

 

[TridenT]

0
80
80

 

[Dr. Zaus]

0
80
80

the total probability of seeing either an Aardvark or (inclusive or) a Bear is .8; so P(Ardvark) + P(Bear) - P(Ardvark AND Bear) = .8

 

[BladeVenom]

Do your own homework.

 

[Dr. Zaus]

Do your own homework.

I already did; turned it in too.

Just thought it was fun.

 

[shortylickens]

I just started Probability yesterday. Not really up to unknown word problems.
Will ask the teacher on Monday.

 

[mjrpes3]

if A then (.65 * B)
.8 = A | B

A & B = .65 * .8
A & !B = (1 - .65) * .8
!A & B = Not Determinable

I think I'm reading your second sentence wrong.

 

[Dr. Zaus]

if A then (.65 * B)
.8 = A | B

A & B = .65 * .8
A & !B = (1 - .65) * .8
!A & B = Not Determinable

I think I'm reading your second sentence wrong.

You are correct SR!

 

[mjrpes3]

Oh, OK then

 

[Dr. Zaus]

Oh, OK then

But my professor disagrees with you...

Of course who is he to argue now that there are two of us!

 

[Numenorean]

All probabilities are 50%. Something either occurs or it does not.

 

[olds]

All probabilities are 50%. Something either occurs or it does not.

This.
Some people think too much.

 

[DCal430]

what do you mean ardvarks do not lead to bears and bears do not lead to ardvarks. I am confused at what that statement means.

 

[Dr. Zaus]

what do you mean ardvarks do not lead to bears and bears do not lead to ardvarks. I am confused at what that statement means.

A and B are independent; that is seeing an Ardvark does not cause seeing a Bear and vice versa.

 

[DCal430]

P(B|A) = P(B) by independence of A and B
P(B) = 0.65
P(!B) = 1 - P(B)
P(!B) = 0.35
1- P(A or B) -> !P(A or B) = P(!A and !B)
P(!A and !B) = 0.20
P(!A) = P(!A and !B)/P(!B) by independence of A and B
P(!A) = 0.20/0.35
P(A) = 0.15/0.35

P(A and B) = 0.65*0.15/0.35
P(!A and B) = 0.65*0.20/0.35
P(A and !B) = 0.35*0.15/0.35

 

[Dr. Zaus]

^ can you explain why I was confused and thought that there were numerous answers?

I kept the ratio constant as demanded and the total volume at .8 of the universe and had multiple answers...

does independence of B from A mean that they don't overlap?

 

[DCal430]

^ can you explain why I was confused and thought that there were numerous answers?

I kept the ratio constant as demanded and the total volume at .8 of the universe and had multiple answers...

does independence of B from A mean that they don't overlap?

So I assume you understand that because A and B are independent than Probability of seeing a bear given that you seen an ardvark is the same as the probability of seeing a bear. P(B) = P(B|A) = 0.65

No if they didn't overlap then they are not indpendent.

Independent means the following are all true:

IF A and B are independent then:
P(A|B) = P(A)
P(A and B) = P(A)*P(B)

This is what defines inpdendence, if one so is the other statement.

 

[drebo]

50/50.

Either it will or it won't.

That is the answer to any "probability" problem.

 

[DCal430]

If you plug in my result into this formula:

P(Ardvark) + P(Bear) - P(Ardvark AND Bear) = .8

You would see that it works.

 

[DCal430]

50/50.

Either it will or it won't.

That is the answer to any "probability" problem.

So I spent years of studying probability and statistics for no reason then.

 

[LordMorpheus]

50/50.

Either it will or it won't.

That is the answer to any "probability" problem.

50/50 chance of getting hit by lightning on a sunny day?

 

[DrPizza]

50/50.

Either it will or it won't.

That is the answer to any "probability" problem.

Now I know why morons waste money playing the lottery - it's a 50/50 chance - either they'll win, or they won't.

 

[Zeze]

I know I'm wrong but why isn't the second answer 28%?

1. Seeing Aardvark chance = 65%.
2. The chance it doesn't come with bear = 20%
3. .65 x .2 = 28%

 

[drebo]

So I spent years of studying probability and statistics for no reason then.

Yep. Pretty much.

50/50 chance of getting hit by lightning on a sunny day?

Either you will or you won't. 50/50.

Now I know why morons waste money playing the lottery - it's a 50/50 chance - either they'll win, or they won't.

Indeed. ^_^