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!

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- Nov 22nd 2009, 07:05 AMlisa1984wilsonProbabiltiy:
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, 07:54 AMFocus
a) $\displaystyle \mathbb{P}(A \cup B)=\mathbb{P}(A)+\mathbb{P}(B)-\mathbb{P}(A\cap B)$

b),c)$\displaystyle \mathbb{P}(A|B)=\frac{\mathbb{P}(A \cap B)}{\mathbb{P}(B)}$

d) Independence (probability theory) - Wikipedia, the free encyclopedia - Nov 22nd 2009, 07:56 AMCaptainBlack
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, 08:43 AMmatheagle

from that link....

Two events*A*and*B*are**independent**if and only if Pr(*A*∩*B*) = Pr(*A*)Pr(*B*). - Nov 22nd 2009, 02:46 PMlisa1984wilson
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, 02:49 PMmatheagle
- Nov 22nd 2009, 02:54 PMlisa1984wilson
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, 05:26 PMmatheagle