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`

Answer

To find the probability that the race will be won by horse A or horse B, we can follow these steps:

### Step 1: Identify the probabilities
The probability of horse A winning the race is given as \( P(A) = \frac{1}{5} \) and the probability of horse B winning the race is \( P(B) = \frac{1}{6} \).

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

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

### Step 4: Find a common denominator
To add the fractions, we need a common denominator. The least common multiple of 5 and 6 is 30. Thus, we convert the fractions:
\[ \frac{1}{5} = \frac{6}{30} \quad \text{and} \quad \frac{1}{6} = \frac{5}{30} \]

### 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
Therefore, the probability that the race will be won by horse A or horse B is:
\[ P(A \text{ or } B) = \frac{11}{30} \]