events A B and C are exhaustive events the odds against A are 8:3 and in favour of - Maths - Probability

Question

events A B and C are exhaustive events the odds against A are 8:3
and in favour of B are 2:5 find the odds in favour of C

Priyanka Kedia · Accepted Answer

Given, three events A,B, and C are exhaustive
 So,PA+PB+PC=1     
1Now,Odds against A are 8:3, so,PA=38+3=311And, Odds against B are 5:2, so,PB=25+2=27Put these values in equation 1,311+27+PC=1⇒PC=3477⇒PC¯=1-PC=1-3477=4377Thus, odds in favour of C are PC:PC=3477:4377=34:43

events A B and C are exhaustive events . the odds against A are 8:3 and in favour of B are 2:5. find the odds in favour of C