	Four hundred people attending a party are each given a number, 1 to 400, for a
	door-prize drawing.  One number is drawn at random to determine the winner.
	Find the probability that the number drawn:
is  123



Consists of the same three digits


has two digits and ends in 9



does not contain an 8



is an even number or greater than 390.



Let's calculate the probabilities for each condition:

### 1. **The number drawn is 123:**
There is exactly one way for the number drawn to be 123, and there are 400 possible numbers.

\[
\text{Probability} = \frac{1}{400}
\]

### 2. **The number consists of the same three digits:**
The only numbers between 1 and 400 that consist of three identical digits are 111, 222, and 333.

There are 3 such numbers out of 400, so the probability is:

\[
\text{Probability} = \frac{3}{400}
\]

### 3. **The number has two digits and ends in 9:**
The two-digit numbers that end in 9 are: 19, 29, 39, 49, 59, 69, 79, 89, and 99. 

There are 9 such numbers out of 400, so the probability is:

\[
\text{Probability} = \frac{9}{400}
\]

### 4. **The number does not contain an 8:**
We need to count how many numbers between 1 and 400 do not contain the digit 8 in any position.

- From 1 to 99: there are 81 numbers without an 8.
- From 100 to 199: there are 90 numbers without an 8.
- From 200 to 299: there are 90 numbers without an 8.
- From 300 to 399: there are 90 numbers without an 8.
- From 400: there is 1 number (400) that does not contain an 8.

So the total number of numbers without an 8 is:

\[
81 + 90 + 90 + 90 + 1 = 352
\]

Thus, the probability is:

\[
\text{Probability} = \frac{352}{400} = 0.88
\]

### 5. **The number is even or greater than 390:**
- There are 200 even numbers between 1 and 400.
- The numbers greater than 390 are: 391, 392, 393, 394, 395, 396, 397, 398, 399, 400. These are 10 numbers.
- We need to subtract the overlap (even numbers greater than 390), which are: 392, 394, 396, 398, 400. These are 5 numbers.

So, the total number of favorable outcomes is:

\[
200 + 10 - 5 = 205
\]

Thus, the probability is:

\[
\text{Probability} = \frac{205}{400} = 0.5125
\]

---

Let me know if you need further details! Here are 5 related questions:

1. How would the probabilities change if 500 people attended the party?
2. What is the probability of drawing a number with a repeated digit?
3. What is the probability of drawing a prime number?
4. Can you calculate the probability of drawing a number divisible by 5?
5. How does the probability change if the drawn number must be odd and less than 100?

**Tip:** When solving probability problems, always ensure that the total number of possible outcomes is well understood and fixed.

Four hundred people attending a party are each given a number, 1 to 400, for a door-prize drawing. One number is drawn at random to determine the winner. Find the probability that the number drawn: is 123, consists of the same three digits, has two digits and ends in 9, does not contain an 8, or is an even number or greater than 390.

This problem involves calculating probabilities for various conditions, including drawing the number 123, numbers with specific digits, and numbers that meet specific criteria from a total of 400 attendees. Learn how to use basic probability concepts to solve the problem, suitable for students in Grades 10-12.

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