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) = [tex]\frac{a}{b}[/tex] ÷ (
So that;
Odd that Romance will win = 2:3
Pr(R) = [tex]\frac{2}{3}[/tex] ÷ (
= [tex]\frac{2}{3}[/tex] ÷ [tex]\frac{5}{3}[/tex]
= [tex]\frac{2}{5}[/tex]
Odd that Downhill will win = 1:2
Pr(D) = [tex]\frac{1}{2}[/tex] ÷ (
= [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{3}{2}[/tex]
= [tex]\frac{1}{3}[/tex]
The probability that either Romance or Downhill will win is;
Pr(R) + Pr(D) = [tex]\frac{2}{5}[/tex] + [tex]\frac{1}{3}[/tex]
= [tex]\frac{11}{15}[/tex]
The probability that neither Romance nor Downhill will win is;
Pr(neither R nor D) = (1 - [tex]\frac{11}{15}[/tex])
= [tex]\frac{4}{15}[/tex]
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)
= [tex]\frac{11}{15}[/tex] ÷ [tex]\frac{4}{15}[/tex]
= [tex]\frac{11}{4}[/tex]
Therefore, odds to be given for an event that either Romance or Downhill wins is 11:4
