Question

In a horse race, the odds that Romance will win are listed as 2 : 3 and that Downhill will win are
1:2. What odds should be given for the event that either Romance or Downhill wins? (3 mks)
QUESTION FOUR​

Answer 1

Answer:

The odds for the event that either Romance or Downhill wins is 11/4

Explanation:

The odds that Romance will win is 2: 3

The odds that Downhill will win is 1:2

$P(event) = \frac{Odd(event)}{1 + Odd(event)}$

Where P(event) = Probability that an event occurs

Odd(event) = The odds that an event occurs

Calculate the Probability that Romance wins, P(R):

$P(R) = \frac{2/3}{2/3 + 1} \\P(R) = 2/5$

Calculate the probability that Downhill wins, P(D):

$P(D) = \frac{1/2}{1/2 + 1} \\P(D) = 1/3$

Calculate the Probability that either Romance or Downhill wins, P(R or D):

P(R or D) = P(R) + P(D)

P(R or D) = 2/5 + 1/3

P(R or D) = 11/15

$P(R or D) = \frac{Odd(R or D)}{1 + Odd(R or D)} \\\\11/15 = \frac{Odd(R or D)}{1 + Odd(R or D)}$

$\frac{11}{15} + \frac{11}{15}[ Odd(R or D)] = Odd(R or D)\\\\\frac{4}{15}[ Odd(R or D)] = \frac{11}{15}\\\\\\Odd(R or D) = \frac{11}{15} * \frac{15}{4}\\\\Odd(R or D) = 11/4$