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