Question 1182451
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Let A and B be events with P(A)=1/2, P(B)=1/3 and P(A∩B)=1/4. Find
i) P(A | B)
ii) P(B | A)
iii) P(A U B)
iv) P(A'| B')
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(i)    P(A|B) = P(A∩B)/P(B) = {{{((1/4))/((1/3))}}} = {{{3/4}}}.


(ii)   P(B|A) = P(A∩B)/P(A) = {{{((1/4))/((1/2))}}} = {{{2/4}}} = {{{1/2}}}.


(iii)  P(AUB) = P(A) + P(B) - P(A∩B) = {{{1/2}}} + {{{1/3}}} - {{{1/4}}} = {{{6/12 + 4/12 - 3/12}}} = {{{7/12}}}.


(iv)  P(A'|B') = P(A'∩B')/P(B') = (1-P(AUB))/(1-P(B)) = {{{((1-7/12))/((1-1/3))}}} = {{{((5/12))/((2/3))}}} = {{{15/24}}}= {{{5/8}}}.
</pre>

Solved.