probability?

Question

Let P(A)=1/3, P(B)=3/10, P(A|B)=2/3...Find P(A U B).
I am not understanding this stuff...your help is appreciated!

Answer 1

1/15
Start with the big one -- three chances in ten
then the easy one -- one chance in three
ok -- now you are at 1 chance in ten which is the same as 3 chances in 30
take 2/3 of that and you have 2 of 30 or 1 in 15.

Or you could multiply 1 times 3 tines 2 which is 6
and divide by 3 times 10 times 3 which is 90.
Divide 6 by 90 and get 1/15.

Answer 2

The formula for a conditional probability is:
P(A|B)=(P(AintersectionB))/(P(B))
Using this you find P(AintB) = P(A|B)*P(B) = 6/30 = 1/5.
Now, you can use the following formula to find the union of A and B, i.e. P(AUB) = P(A) + P(B) - P(AintB) = 1/3 + 3/10 - 1/5 = 13/30.

Hope that helped. Good luck with everything.