# Probabiltiy:

• Nov 22nd 2009, 08:05 AM
lisa1984wilson
Probabiltiy:
Given P(A) = .4, P(B) = .5, and P(A or B) = .7,
a)find P(A and B)

b)find P(A/B)

c)find P(B/A)

d)are A and B independent? Why, or why not?

Had trouble with this of probability question on my exam..any help is much appreciated...Thanks!
• Nov 22nd 2009, 08:54 AM
Focus
a) $\mathbb{P}(A \cup B)=\mathbb{P}(A)+\mathbb{P}(B)-\mathbb{P}(A\cap B)$
b),c) $\mathbb{P}(A|B)=\frac{\mathbb{P}(A \cap B)}{\mathbb{P}(B)}$
d) Independence (probability theory) - Wikipedia, the free encyclopedia
• Nov 22nd 2009, 08:56 AM
CaptainBlack
Quote:

Originally Posted by lisa1984wilson
Given P(A) = .4, P(B) = .5, and P(A or B) = .7,
a)find P(A and B)

b)find P(A/B)

c)find P(B/A)

d)are A and B independent? Why, or why not?

Had trouble with this of probability question on my exam..any help is much appreciated...Thanks!

Draw a Venn diagram, and use it to determine P(A and B) (that is A intersection B)

That should allow you to answer a), b) and c). For d) you need to determine if:

P(A and B)=P(A)P(B)

(when A and B will be independednt and not if this does not hold) and you have sufficient data to do so.

CB
• Nov 22nd 2009, 09:43 AM
matheagle
Quote:

Originally Posted by Focus
I don't believe this is a university question but here are some hints;

a) $\mathbb{P}(A \cup B)=\mathbb{P}(A)+\mathbb{P}(B)-\mathbb{P}(A\cap B)$
b),c) $\mathbb{P}(A|B)=\frac{\mathbb{P}(A \cap B)}{\mathbb{P}(B)}$
d) Independence (probability theory) - Wikipedia, the free encyclopedia

Two events A and B are independent if and only if Pr(AB) = Pr(A)Pr(B).
• Nov 22nd 2009, 03:46 PM
lisa1984wilson
Given P(A) = .4, P(B) = .5, and P(A or B) = .7,

a)find P(A and B) P(A and B)=P(A)+P(B)-P(A or B)=.4+.5-.7=.2

b)find P(A/B) P(A/B)=P(A or B)/P(B)=.7/.5=1.4

c)find P(B/A) P(B/A)=P(A or B)/P(A)=.7/.4=1.75

d)are A and B independent? Why, or why not?

Not independent because P(A or B) does not equal P(A)P(B)
• Nov 22nd 2009, 03:49 PM
matheagle
Quote:

Originally Posted by lisa1984wilson
Given P(A) = .4, P(B) = .5, and P(A or B) = .7,

a)find P(A and B) P(A and B)=P(A)+P(B)-P(A or B)=.4+.5-.7=.2

b)find P(A/B) P(A/B)=P(A or B)/P(B)=.7/.5=1.4

c)find P(B/A) P(B/A)=P(A or B)/P(A)=.7/.4=1.75

d)are A and B independent? Why, or why not?

Not independent because P(A or B) does not equal P(A)P(B)

OR is union while AND is intersection.
you need AND
• Nov 22nd 2009, 03:54 PM
lisa1984wilson
I'm sorry...I'm just having trouble with this one, I did get this wrong on my exam. I'm just trying to get it right so can practice it before my next exam.
• Nov 22nd 2009, 06:26 PM
matheagle
Quote:

Originally Posted by lisa1984wilson
Given P(A) = .4, P(B) = .5, and P(A or B) = .7,

a) P(A and B)=P(A)+P(B)-P(A or B)=.4+.5-.7=.2 YES

b) P(A/B)=P(A or B)/P(B)=.7/.5=1.4>1 means this is WRONG

c) P(B/A)=P(A or B)/P(A)=.7/.4=1.75> 1 means this is WRONG

d)are A and B independent? Why, or why not?

Not independent because P(A or B) does not equal P(A)P(B)

b) P(A/B)=P(A AND B)/P(B)=.2/.5=.4
c) P(B/A)=P(A AND B)/P(A)=.2/.4=.5

They are indeed independent since P(A|B)=P(A) which holds whenever P(AB)=P(A)P(B) same with P(B|A)=P(B)
as I said yesterday.