Question 262826
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.


<a href = "http://people.richland.edu/james/lecture/m170/ch05-rul.html" target = "_blank">http://people.richland.edu/james/lecture/m170/ch05-rul.html</a>


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.