MATH SOLVE

2 months ago

Q:
# 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.)

Accepted Solution

A:

Answer:The required probability is 0.0004995Step-by-step explanation:Consider the provided informationThere 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 [tex]\frac{5}{14}[/tex]Now we have 4 horses left,Probability that out of remaining 4 horses one will be second is [tex]\frac{4}{13}[/tex].The probability that out of remaining 3 horses one will be third is [tex]\frac{3}{12}[/tex].The probability that out of remaining 2 horses one will be fourth is [tex]\frac{2}{11}[/tex].The probability that out of remaining 1 horses one will be fifth is [tex]\frac{1}{11}[/tex].Hence, the total probability is:[tex]\frac{5}{14}\times \frac{4}{13} \times \frac{3}{12} \times \frac{2}{11}\times \frac{1}{10}=0.0004995[/tex]Hence, the required probability is 0.0004995