The probability of a man hitting a target is 1/4. How many times must he fire so that the probability of his hitting the target at lest once is greater than 2/3?

Explanation

To solve the problem, we need to determine how many times a man must fire at a target, given that the probability of hitting the target is \( \frac{1}{4} \), such that the probability of hitting the target at least once is greater than \( \frac{2}{3} \).

### Step-by-Step Solution:

1. **Understanding the Probability of Hitting the Target**:
- The probability of hitting the target in one shot is \( p = \frac{1}{4} \).
- The probability of not hitting the target in one shot is \( q = 1 - p = 1 - \frac{1}{4} = \frac{3}{4} \).

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