Events \(A\) and \(B\) are such that \(\mathrm P(A)=\frac13\), \(\mathrm P(B\mid A)=\frac14\) and \(\mathrm P(A'\cap B')=\frac16\). Find
\(\mathrm P(A\cup B)\),[2]
\(\mathrm P(B)\).[3]
A man writes 5 letters, one each to A, B, C, D and E. Each letter is placed in a separate envelope and sealed. He then addresses the envelopes, at random, one each to A, B, C, D and E.
Find the probability that the letter to A is in the correct envelope and the letter to B is in an incorrect envelope.[1]
Find the probability that the letter to A is in the correct envelope, given that the letter to B is in an incorrect envelope.[3]
Find the probability that both of the letters to A and B are in incorrect envelopes.[5]
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Answer:(a)(i) \(5/6\), (ii) \(7/12\). (b)(i) \(3/20\), (ii) \(3/16\), (iii) \(13/20\).