1)Express the following statements concerning the three events A, B, and T in terms of the occurrence of a single event: (a) none occurs, (b) only one occurs, (c) at least one occur, (d) at most two occur, (e) two and only tow occur, (f) A and B occur but T does not occur. Solution a> 1-P(AUBUT) b> P(A)+P(B)+P(C)-P(AnB)-P(BnT)-P(TnA)+P(AnBnT) c> 1- P\'(AUBUT) d> P\'(AUBUC)+P(AnB)+P(TnA)+P(BnT) e> P(AnB)+P(BnT)+P(TnA)- 3P(AnBnT) c> P((AUB)nT\').

1. 1)Express the following statements concerning the three events A, B, and T in terms of the
occurrence of a single event: (a) none occurs, (b) only one occurs, (c) at least one occur, (d) at
most two occur, (e) two and only tow occur, (f) A and B occur but T does not occur.
Solution
a> 1-P(AUBUT) b> P(A)+P(B)+P(C)-P(AnB)-P(BnT)-P(TnA)+P(AnBnT) c> 1-
P'(AUBUT) d> P'(AUBUC)+P(AnB)+P(TnA)+P(BnT) e> P(AnB)+P(BnT)+P(TnA)-
3P(AnBnT) c> P((AUB)nT')