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.