Question

there are three events A B and C one of which must only one can happen the odds are 8 to 3 against A, 5 to 2 against B , then odds against C is

Answer 1

if three events A B C
then sum of all probablities of all possible events is 1
 probablity of favour of A=1-odds against A
                                       =1-3/8
                                       =5/8
 probablity of favour of B=1-odds against  B
                                         =1-2/5
                                         =3/5
 probablity of odds A+ probablity of odds B+ probablity of oddsC=1
3/8+2/5+ probablity of oddsC=1
probablity of oddsC=1-31/40
                              =9/40