a horse race has 14 entries and one person owns 3 of those horses. assuming that there are no ties, what is the probability that those three horses finish first, second and third?
To calculate the probability of those three horses finishing first, second, and third in a horse race, we need to consider the total number of possible outcomes and the desired outcomes.
Total number of outcomes:
Since there are 14 horses participating in the race, the total number of outcomes is given by the number of horses factorial, which is denoted as 14!.
Desired outcomes:
The three horses owned by the person must finish in the specific order of first, second, and third. Therefore, there is only one desired outcome.
To calculate the probability, we divide the number of desired outcomes by the total number of outcomes. So, the probability (P) is:
P = (number of desired outcomes) / (total number of outcomes)
P = 1 / 14!
To simplify this, we need to calculate 14! (read as "14 factorial"):
14! = 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
Using a calculator or a computer program, we can find the value of 14! to be:
14! = 87,178,291,200
Now we can calculate the probability:
P = 1 / 87,178,291,200
The probability that those three horses finish first, second, and third is approximately equal to:
P ≈ 0.00000000000114675
So, the probability is very low, indicating that the chance of those three horses finishing in first, second, and third place is highly unlikely.
To calculate the probability of those three horses finishing first, second, and third, we can use the concept of independent events.
First, we need to determine the total number of possible outcomes. Since there are 14 entries in the race, the total number of outcomes is 14 factorial (14!).
Next, we need to determine the number of favorable outcomes where the person's three horses finish first, second, and third. The first horse has a 1/14 chance of finishing first, the second horse has a 1/13 chance of finishing second, and the third horse has a 1/12 chance of finishing third. Therefore, the number of favorable outcomes is (1/14) * (1/13) * (1/12).
Finally, we divide the number of favorable outcomes by the total number of possible outcomes to find the probability:
Probability = Number of favorable outcomes / Number of possible outcomes
= (1/14) * (1/13) * (1/12) / 14!
Using a calculator to simplify the factorial expression, we get:
Probability ≈ 0.000114
Therefore, the probability that those three horses finish first, second, and third is approximately 0.000114 or 0.0114%.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
1/14 * 1/13 * 1/12 = ?