how many tries to get a guaranteed 0.5% chance

To determine the number of tries required to have a guaranteed chance of achieving an event with a 0.5% probability, we need to calculate the number of trials required to ensure that the cumulative probability of success is very close to 100%. This involves using the concept of complementary probability.

### Step-by-Step Calculation:

1. **Probability of Failure in a Single Try**:  
   The probability of **not** achieving the event in a single try is \( 1 - 0.005 = 0.995 \).

2. **Probability of Failure After \( n \) Tries**:  
   The probability of **not** achieving the event after \( n \) tries is \( 0.995^n \).

3. **Probability of Success After \( n \) Tries**:  
   The probability of achieving the event at least once after \( n \) tries is \( 1 - 0.995^n \).

4. **Determine \( n \) for Near-Guaranteed Success**:  
   We want to find \( n \) such that the probability of success is close to 100%, say 99.9%.

   Therefore, solve \( 1 - 0.995^n = 0.999 \).

   \[
   0.995^n = 0.001
   \]

   Take the natural logarithm on both sides:

   \[
   n \cdot \ln(0.995) = \ln(0.001)
   \]

   Solve for \( n \):

   \[
   n = \frac{\ln(0.001)}{\ln(0.995)}
   \]

Let's calculate this.You would need approximately **1,378 tries** to achieve a near-guaranteed 99.9% chance of success for an event with a 0.5% probability per try.

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How does increasing the probability per try affect the number of required trials?
2. What if the desired success probability is 99% instead of 99.9%?
3. How does the number of trials change if the event probability per try is 1%?
4. What is the probability of success after 500 tries with a 0.5% chance per try?
5. How do different statistical distributions affect these calculations?

**Tip:** When dealing with low probabilities, even a small increase in the success rate per trial can significantly reduce the number of required trials for high-confidence outcomes.

Learn how to calculate the number of tries needed to achieve a guaranteed 99.9% chance of success for an event with a 0.5% probability per try. This detailed solution uses complementary probability and logarithmic calculations to determine approximately 1,378 tries required. Explore related questions on probability and statistical distributions.

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