In a cricket match, a batsman hits a boundary 16 times out of 30 balls he plays. Find the probability that he does not hit a boundary.

Options

A. `7//15`
B. `8//15`
C. `2//15`
D. `12//15`

Answer

To find the probability that the batsman does not hit a boundary, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Total Balls Played**:
The batsman played a total of 30 balls.

2. **Identify Balls with Boundaries**:
The batsman hit a boundary 16 times.

3. **Calculate Balls without Boundaries**:
To find the number of balls on which the batsman did not hit a boundary, subtract the number of boundaries from the total balls played:
\[ \text{Balls without boundaries} = \text{Total balls} - \text{Balls with boundaries} = 30 - 16 = 14 \]

4. **Calculate Probability of Not Hitting a Boundary**:
The probability of an event is given by the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} \]
Here, the number of favorable outcomes (balls without boundaries) is 14, and the total outcomes (total balls played) is 30. Thus, the probability is:
\[ P(\text{Not hitting a boundary}) = \frac{14}{30} \]

5. **Simplify the Fraction**:
To simplify \(\frac{14}{30}\), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 2:
\[ \frac{14 \div 2}{30 \div 2} = \frac{7}{15} \]

6. **Final Answer**:
Therefore, the probability that the batsman does not hit a boundary is:
\[ \frac{7}{15} \]