
If there is a 1 in 2300 chance that you will pick the numbers correctly in​ tonight's lottery, what is the probability that you will not pick the numbers​ correctly?

To calculate the probability that you will **not** pick the numbers correctly, we can use the concept of complementary probability.

Given:
- The probability of picking the numbers correctly is \( P(\text{correct}) = \frac{1}{2300} \).

The probability of not picking the numbers correctly is the complement of this, which is:

\[
P(\text{not correct}) = 1 - P(\text{correct}) = 1 - \frac{1}{2300}
\]

Let's calculate:

\[
P(\text{not correct}) = \frac{2300 - 1}{2300} = \frac{2299}{2300}
\]

Thus, the probability that you will **not** pick the numbers correctly is \( \frac{2299}{2300} \), or approximately 0.99957.

### Do you want more details or have any questions?

Here are 5 related questions you might find useful:
1. What is complementary probability, and how is it used in other problems?
2. How would the probability change if the odds were increased to 1 in 5000?
3. Can we express this probability as a percentage?
4. What is the probability of winning the lottery if the odds are 1 in 1 million?
5. How would you calculate the probability of winning two lotteries back-to-back?

**Tip:** The sum of the probabilities of an event and its complement is always equal to 1.

If there is a 1 in 2300 chance that you will pick the numbers correctly in​ tonight's lottery, what is the probability that you will not pick the numbers​ correctly?

Learn how to calculate the probability of not winning the lottery when the odds are 1 in 2300. Using complementary probability, this step-by-step solution shows how to find the chance that you will not pick the correct numbers. Perfect for students in Grades 9-10.

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