SOLUTION: I don't even know how to set up this problem. I am not finding examples, can you help please? Events A and B are mutually exclusive events defined on a common sample space. If

Question 262826: I don't even know how to set up this problem. I am not finding examples, can you help please?
Events A and B are mutually exclusive events defined on a common sample space. If P (A) = 0.3
and P(A or B) = 0.75, find P(B).
(B) Events A and B are defined on a common sample space. If P(A) = 0.30, P(B) = 0.50, and P(A or
B) = 0.72, find P(A and B)
Found 2 solutions by drk, Theo:
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
We have a general formula to help us:
(i)
p(a u B) means probability of A union B. Union is another word for "OR"
p(A n B) means probability of A intersection B. Intersection is another word for "AND"
since events A and B are mutually exclusive, there will be no overlap and there fore, p(A n B) = 0.
From above and this information, we get
(ii)
solving for p(B), we get
(iii)
-----
part (B):
using the same formula as
(iv)
and the given information, we get
(i)
we get

this means there is a slight overlap of the 2 sets.
hope this helps.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
p(a or b) = p(a) + p(b) if a and b are mutually exclusive.

if p(a) = .3 and p(a or b) = .75, then p(b) must be equal to .75 - .3 = .45

you get p(a or b) = p(a) + p(b) = .3 + .45 = .75

your second problem states that:

p(a) = .3
p(b) = .5
p(a or b) = .72

find p(a and b)

in this example, apparently a and b are not mutually exclusive.

the formula becomes:

p (a or b) = p(a) + p(b) - p(a and b)

based on that, your equation becomes:

.72 = .3 + .5 - p(a and b)

this becomes:

.72 = .8 - p(a and b)

add p(a and b) to both sides of this equation and subtract .72 from both sides of this equation to get:

p(a and b) = .8 - .72 = .08

your answer is p(a and b) = .08

here's a reference that shows you how it works.

http://people.richland.edu/james/lecture/m170/ch05-rul.html

what is happening when events a and b are not mutually exclusive is that you can have cases where both events a and b occur simultaneously.

when that happens, they are being counted twice if you just add up p(a) + p(b).

by subtracting p(a and b), you are eliminating the double counting.

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