In a horse -race, the probabilities to win the race for three horses A,B and C are `1/4,1/5` and `1/6` respectively. Find the probability to win the race of any one horse.

Explanation

To solve the problem of finding the probability that at least one horse wins in a horse race involving horses A, B, and C, we can follow these steps:

### Step 1: Write down the given probabilities
- The probability of horse A winning the race, \( P(A) = \frac{1}{4} \)
- The probability of horse B winning the race, \( P(B) = \frac{1}{5} \)
- The probability of horse C winning the race, \( P(C) = \frac{1}{6} \)

### Step 2: Find the total probability of winning
To find the probability that at least one horse wins, we can use the formula for the probability of the union of mutually exclusive events. The formula is:
\[ P(A \cup B \cup C) = P(A) + P(B) + P(C) \]
Since the horses cannot win at the same time, we can ignore the intersection probabilities.

### Step 3: Calculate the least common multiple (LCM)
To add the fractions, we need a common denominator. The denominators are 4, 5, and 6. The LCM of these numbers is 60.

### Step 4: Convert each probability to have the common denominator
- For horse A:
\[ P(A) = \frac{1}{4} = \frac{15}{60} \]
- For horse B:
\[ P(B) = \frac{1}{5} = \frac{12}{60} \]
- For horse C:
\[ P(C) = \frac{1}{6} = \frac{10}{60} \]

### Step 5: Add the probabilities
Now, we can add the converted probabilities:
\[ P(A \cup B \cup C) = \frac{15}{60} + \frac{12}{60} + \frac{10}{60} = \frac{15 + 12 + 10}{60} = \frac{37}{60} \]

### Final Answer
The probability that at least one horse wins the race is:
\[ \frac{37}{60} \]