The chance of winning the race of the horse A is 1/5 and that of horse B is 1/6. What is the probability that the race will be won by A or B ?

Options

A. `1//30`
B. `1//3`
C. `11//30`
D. `1//15`

Explanation

To solve the problem of finding the probability that the race will be won by either horse A or horse B, we can follow these steps:

### Step 1: Identify the probabilities
We know the probabilities of winning for each horse:
- Probability of horse A winning, \( P(A) = \frac{1}{5} \)
- Probability of horse B winning, \( P(B) = \frac{1}{6} \)

### Step 2: Use the formula for the probability of either event occurring
To find the probability that either horse A or horse B wins, we use the formula:
\[ P(A \text{ or } B) = P(A) + P(B) \]

### Step 3: Substitute the values into the formula
Now, we substitute the probabilities into the formula:
\[ P(A \text{ or } B) = \frac{1}{5} + \frac{1}{6} \]

### Step 4: Find a common denominator
To add these fractions, we need a common denominator. The least common multiple (LCM) of 5 and 6 is 30. We convert each fraction:
\[ \frac{1}{5} = \frac{6}{30} \quad \text{and} \quad \frac{1}{6} = \frac{5}{30} \]

### Step 5: Add the fractions
Now we can add the two fractions:
\[ P(A \text{ or } B) = \frac{6}{30} + \frac{5}{30} = \frac{11}{30} \]

### Step 6: Conclusion
Thus, the probability that the race will be won by either horse A or horse B is:
\[ \boxed{\frac{11}{30}} \]