In a cricket match, a batsman hits a boundary 8 times out of 40 balls he plays. Find the probability that he didn’t hit a boundary.

Options

A. `4/5`
B. `1/5`
C. `3/5`
D. `2/5`

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
The batsman played a total of 40 balls.

### Step 2: Identify the number of boundaries hit
The batsman hit a boundary 8 times.

### Step 3: Calculate the number of balls on which no boundary was hit
To find the number of balls on which the batsman did not hit a boundary, we subtract the number of boundaries from the total number of balls:
\[ \text{Number of balls without boundary} = \text{Total balls} - \text{Number of boundaries} \]
\[ = 40 - 8 = 32 \]

### Step 4: Calculate the probability of not hitting a boundary
The probability of an event is given by the formula:
\[ \text{Probability} = \frac{\text{Number of favorable cases}}{\text{Total number of cases}} \]
In this case, the number of favorable cases (balls without a boundary) is 32, and the total number of cases (total balls) is 40:
\[ \text{Probability of not hitting a boundary} = \frac{32}{40} \]

### Step 5: Simplify the fraction
To simplify \(\frac{32}{40}\), we can divide both the numerator and the denominator by their greatest common divisor, which is 8:
\[ \frac{32 \div 8}{40 \div 8} = \frac{4}{5} \]

### Final Answer
The probability that the batsman did not hit a boundary is \(\frac{4}{5}\).

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