.
(i) Use the general formula of the Probability theory
P(A or B) = P(A) + P(B) - P(A and B).
Substitute the given data to the formula
= + - P(A and B).
It gives you
P(A and B) = = = = . ANSWER
(ii) The given equality P(A|B) = means, by the definition of the conditional probability, that
P(A and B)/P(B) = .
It implies that
P(A and B) = = = . ANSWER
Notice that the given value P(A) = is IRRELEVANT to the solution of the part (ii).
Solved.
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If you want to see many other similar solved problems, look into the lessons
- Elementary operations on sets help solving Probability problems
- Elementary operations on sets help solving Probability problems - REVISITED
- Using general probability formulas for a union or intersection of events
- Conditional probability problems
in this site.