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):
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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