A man can hit a target once in 4 shots. if he fires 4 shot in succession what is probability, atleast he will hit target once.

Answer

To solve the problem step by step, we will find the probability that a man hits a target at least once when he fires 4 shots, given that he can hit the target once in 4 shots.

### Step-by-Step Solution:

1. **Determine the Probability of Hitting the Target**:
The man can hit the target once in 4 shots. Therefore, the probability of hitting the target (P(hit)) is:
\[ P(\text{hit}) = \frac{1}{4} \]

2. **Determine the Probability of Missing the Target**:
The probability of missing the target (P(miss)) is the complement of hitting the target:
\[ P(\text{miss}) = 1 - P(\text{hit}) = 1 - \frac{1}{4} = \frac{3}{4} \]

3. **Calculate the Probability of Missing All Shots**:
If he fires 4 shots, the probability that he misses all of them is:
\[ P(\text{miss all}) = P(\text{miss})^4 = \left(\frac{3}{4}\right)^4 \]
Calculating this gives:
\[ P(\text{miss all}) = \left(\frac{3}{4}\right)^4 = \frac{3^4}{4^4} = \frac{81}{256} \]

4. **Calculate the Probability of Hitting the Target at Least Once**:
The probability of hitting the target at least once is the complement of missing all shots:
\[ P(\text{hit at least once}) = 1 - P(\text{miss all}) = 1 - \frac{81}{256} \]
Simplifying this gives:
\[ P(\text{hit at least once}) = \frac{256 - 81}{256} = \frac{175}{256} \]

### Final Answer:
The probability that he will hit the target at least once when he fires 4 shots is:
\[ \frac{175}{256} \]