Question

QUESTION THREE

Answer 1

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) = $\frac{a}{b}$ ÷ (

So that;

Odd that Romance will win = 2:3

Pr(R) = $\frac{2}{3}$ ÷ (

        = $\frac{2}{3}$ ÷ $\frac{5}{3}$

       = $\frac{2}{5}$

Odd that Downhill will win = 1:2

Pr(D) = $\frac{1}{2}$ ÷ (

        =  $\frac{1}{2}$ ÷ $\frac{3}{2}$

        = $\frac{1}{3}$

The probability that either Romance or Downhill will win is;

Pr(R) + Pr(D) = $\frac{2}{5}$ +  $\frac{1}{3}$

                    = $\frac{11}{15}$

The probability that neither Romance nor Downhill will win is;

Pr(neither R nor D) = (1 - $\frac{11}{15}$)

                               = $\frac{4}{15}$

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)

                               = $\frac{11}{15}$ ÷ $\frac{4}{15}$

                              = $\frac{11}{4}$

Therefore, odds to be given for an event that either Romance or Downhill wins is 11:4