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

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

Step-by-step explanation:

The odds that Romance will win is 2: 3

The odds that Downhill will win is 1:2

`P(event) = (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) = (2/3)/(2/3 + 1) \\P(R) = 2/5`

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

`P(D) = (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) = (Odd(R or D))/(1 + Odd(R or D)) \\\\11/15 = (Odd(R or D))/(1 + Odd(R or D))\\`

`(11)/(15) + (11)/(15)[ Odd(R or D)] = Odd(R or D)\\\\(4)/(15)[ Odd(R or D)] = (11)/(15)\\\\\\Odd(R or D) = (11)/(15) * (15)/(4)\\\\Odd(R or D) = 11/4`