In a cricket match a batsman hits a boundary 6 times out of 20 balls he plays. Find the probability that he did not hit a boundary.

Answer

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

### Step 1: Identify the total number of balls played and the number of boundaries hit.
- The batsman played a total of 20 balls.
- The batsman hit a boundary 6 times.

### Step 2: Calculate the probability of hitting a boundary.
- The probability \( P(E) \) of hitting a boundary is given by the formula:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{n(E)}{n(S)} \]
- Here, \( n(E) = 6 \) (the number of boundaries hit) and \( n(S) = 20 \) (the total number of balls played).
- Therefore, the probability of hitting a boundary is:
\[ P(E) = \frac{6}{20} \]

### Step 3: Simplify the probability of hitting a boundary.
- Simplifying \( \frac{6}{20} \):
\[ P(E) = \frac{3}{10} \]

### Step 4: Calculate the probability of not hitting a boundary.
- The probability of not hitting a boundary, denoted as \( P(E') \), can be calculated using the formula:
\[ P(E') = 1 - P(E) \]
- Substituting the value of \( P(E) \):
\[ P(E') = 1 - \frac{3}{10} \]

### Step 5: Simplify the probability of not hitting a boundary.
- To perform the subtraction:
\[ P(E') = \frac{10}{10} - \frac{3}{10} = \frac{7}{10} \]

### Final Answer:
- Therefore, the probability that the batsman did not hit a boundary is:
\[ \frac{7}{10} \]

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