Question

A​ "trifecta" is a particular horse race in which you win by picking the​ "win," "place," and​ "show" horses​ (the first-,​ second-, and​ third-place winners), in their proper order. If five horses of equal ability are entered in a trifecta​ race, and Tracy selects an​ entry, what is the probability that she will be a​ winner?

Answer 1

The probability that she will be a​ winner is:
`(1)/(60)`

Step-by-step explanation:

Consider the provided information.

A​ "trifecta" is a particular horse race in which you win by picking the​ "win," "place," and​ "show" horses​ (the first-,​ second-, and​ third-place winners), in their proper order.

Five horses of equal ability are entered in a trifecta​ race

First find the sample space as shown:

We have five horses for 1st place, if out of 5 horses one horse comes first then we have 4 horses for the second place.

If out of 4 horses one horse comes second then we have 3 horses for the third place.

Therefore the number of ways are:
`5* 4* 3=60`

There are 60 ways for a horse to come first, second or third.

The actual outcome of the race will only be one of these ways.

Hence, the probability that she will be a​ winner is:
`(1)/(60)`