Two events M and N are such that P(M) = \(\frac{1}{2}\), P(N) = \(\frac{9}{20}\) and P(M ∩ N) = \(\frac{11}{50}\) (a) P(M ∩ N'): (b) P(M' ∩ N)

Assessment: WAEC SSCE - Further Mathematics - 2024 (Essay) Subject: Further Mathematics

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Two events M and N are such that P(M) = \(\frac{1}{2}\), P(N) = \(\frac{9}{20}\) and P(M ∩ N) = \(\frac{11}{50}\)

(a) P(M ∩ N'): (b) P(M' ∩ N)

Answer

Answer Details

Given that: P(M) = \(\frac{1}{2}\), P(N) = \(\frac{9}{20}\) and P(M ∩ N) = \(\frac{11}{50}\)

Using the diagram above

(a) P(M ∩ N') = \(\frac{1}{2} - \frac{11}{50}\) = \(\frac{25 - 11}{50}\) = \(\frac{14}{50}\) = \(\frac{7}{25}\)

(b) P(M' ∩ N) = \(\frac{9}{20} - \frac{11}{50}\) = \(\frac{45 - 22}{100}\) = \(\frac{23}{100}\).

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