Region probabilities in a two-event Venn diagram from a union and an intersection, and the probability of a complement
Region probabilities in a two-event Venn diagram from a union and an intersection, and the probability of a complement
6 marks
Two events \(A\) and \(B\) are represented in the Venn diagram below, in which \(m\), \(n\), \(p\) and \(q\) are the probabilities of the four regions. It is known that \(P(A)=0.3\), \(P(A\cup B)=0.6\) and \(P(A\cap B)=0.1\).
- Write down the value of \(n\).
- Find the values of \(m\), \(p\) and \(q\).[4]
- Find \(P(B')\).[2]
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Answer:(a)(i) \(n = 0.1\)
(a)(ii) \(m = 0.2; p = 0.3; q = 0.4\)
(b) \(P(B') = 0.6\)
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