Problem 1. A boy has a fever after coming home in the afternoon.His mother thinks that it could be related to the following threepossible reasons: A : He plays football in the rain, B : He takes acold water shower after playing, C : He eats too many icecreams.
(iii) The mother has 80% confidence that her son’s fever iscaused by at least one of the three reasons. She further estimatesthat the probabilities of the three individual reasons are 0.5,0.5, 0.2 respectively, and she believes that they are pair- wiselyindependent. Are the three reasons mutually independent?
(iv) Suppose that the mother is 100% sure that her son’s feveris caused by at least one of the three reasons. Moreover, shebelieves that they are mutually inde- pendent although she doesn’tknow the exact probabilities of any of the individual reasons.After a moment’s thought, she tells her son that one of the threereasons must be certain (that is, one of P(A) = 1 or P(B) = 1 orP(C) = 1 must be true)! Should the boy believe his mother’sassertion?
