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!
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
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
from that link....
Two events A and B are independent if and only if Pr(A ∩ B) = Pr(A)Pr(B).
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)