Question

QUESTION THREE

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)
OUTSTION FOUR​

Answer 1

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

Step-by-step explanation:

Given an odd, r = a : b. The probability of the odd, r can be determined by;

Pr(r) =
`(a)/(b)` ÷ (

So that;

Odd that Romance will win = 2:3

Pr(R) =
`(2)/(3)` ÷ (

=
`(2)/(3)` ÷
`(5)/(3)`

=
`(2)/(5)`

Odd that Downhill will win = 1:2

Pr(D) =
`(1)/(2)` ÷ (

=
`(1)/(2)` ÷
`(3)/(2)`

=
`(1)/(3)`

The probability that either Romance or Downhill will win is;

Pr(R) + Pr(D) =
`(2)/(5)` +
`(1)/(3)`

=
`(11)/(15)`

The probability that neither Romance nor Downhill will win is;

Pr(neither R nor D) = (1 -
`(11)/(15)`)

=
`(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)

=
`(11)/(15)` ÷
`(4)/(15)`

=
`(11)/(4)`

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