Question

A horse race has 14 entries and one person owns 5 of those horses. Assuming that there are no​ ties, what is the probability that those five horses finish first comma second comma third comma fourth comma and fifth ​(regardless of​ order)? The probability that the five horses finish first comma second comma third comma fourth comma and fifth is nothing . ​(Round to four decimal places as​ needed.)

Answer 1

The required probability is 0.0004995

Explanation:

Consider the provided information

There are 14 horses and one person owns 5 of those horses.

We need to find the number of ways in which 5 horses finish first, second , third, fourth, and fifth.

Each horse has the same probability of winning,

Therefore, the required probability is:

The probability that one of those 5 horses will be first is
`(5)/(14)`

Now we have 4 horses left,

Probability that out of remaining 4 horses one will be second is
`(4)/(13)`.

The probability that out of remaining 3 horses one will be third is
`(3)/(12)`.

The probability that out of remaining 2 horses one will be fourth is
`(2)/(11)`.

The probability that out of remaining 1 horses one will be fifth is
`(1)/(11)`.

Hence, the total probability is:

`(5)/(14)* (4)/(13) * (3)/(12) * (2)/(11)* (1)/(10)=0.0004995`

Hence, the required probability is 0.0004995