Answer:
Odds to be given for an event that either Romance or Downhill wins is 11:4
Explanation:
Given an odd, r = a : b. The probability of the odd, r can be determined by;
Pr(r) =
÷ (
So that;
Odd that Romance will win = 2:3
Pr(R) =
÷ (
=
÷ 
= 
Odd that Downhill will win = 1:2
Pr(D) =
÷ (
=
÷ 
= 
The probability that either Romance or Downhill will win is;
Pr(R) + Pr(D) =
+ 
= 
The probability that neither Romance nor Downhill will win is;
Pr(neither R nor D) = (1 -
)
= 
The odds to be given for an event that either Romance or Downhill wins can be determined by;
= Pr(Pr(R) + Pr(D)) ÷ Pr(neither R nor D)
=
÷ 
= 
Therefore, odds to be given for an event that either Romance or Downhill wins is 11:4