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The problem asks to find the probability $ P(A) $, where $ A $ is the event of winning a lottery with 5,760 possible outcomes.

### Steps:
1. Since only **one of the 5,760 possible outcomes** will be a winning outcome, the probability of winning, $ P(A) $, is simply the ratio of favorable outcomes (1) to the total outcomes (5,760).

\[
P(A) = \frac{1}{5760}
\]

2. We can now compute the value of $ P(A) $:

\[
P(A) = 0.00017361
\]

Thus, the value of $ P(A) $, rounded to five decimal places, is:

\[
P(A) = 0.00017
\]

### Would you like any further clarification or details?

Here are some related questions:
1. How does the total number of outcomes in a lottery change with more digits?
2. What is the probability of losing the lottery with these 5,760 outcomes?
3. How does allowing repetition of digits affect the total number of possible outcomes?
4. What is the effect of adding more possible numbers (e.g., increasing the digits from 0-9 to 0-99)?
5. How would you calculate the odds if you placed multiple bets instead of one?

**Tip:** In probability, always check if events are mutually exclusive or independent, as this influences how probabilities combine.

Let A denote the event of placing a $1 straight bet on a certain lottery and winning. Suppose that, for this particular lottery, there are 5,760 different ways that you can select the four digits (with repetition allowed) in this lottery, and only one of those four-digit numbers will be the winner. What is the value of P(A)?

Find the probability P(A) of winning a lottery with 5,760 possible outcomes by using basic probability concepts. This problem involves calculating the probability of a single favorable outcome among multiple possibilities and is suitable for students in Grades 10-12.

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