Question 262826
We have a general formula to help us:
(i) {{{p(A u B) = p(A) + p(B) - p(A n B)}}}
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) {{{.75 = .3 + p(B) + 0}}}
solving for p(B), we get
(iii) {{{p(B) = .45}}}
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part (B):
using the same formula as
(iv) {{{p(A u B) = p(A) + p(B) - p(A n B)}}}
and the given information, we get
(i) {{{.72 = .30 + .50 - p(A n B)}}}
we get
{{{p(A n B) = .08}}}
this means there is a slight overlap of the 2 sets.
hope this helps.