Question

A lottery game has balls numbered 1 through 21. What is the probability of selecting an even numbered ball or a 13​?

Answer 1

To find the probability of selecting an even numbered ball or the number 13 in a lottery game with balls numbered from 1 to 21, we can follow these steps:

1. **Identify the total number of balls.**
There are 21 balls in total (numbered 1 through 21).

2. **Identify the even numbered balls from 1 to 21.**
The even numbered balls are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.
That gives us 10 even numbered balls.

3. **Identify the event that includes the number 13.**
The inclusion of the number 13 is an additional single outcome. Since 13 is not even, we must ensure we do not double-count it.

4. **Combine the events (even numbered balls or the number 13):**
- Total even numbered balls = 10
- The number 13 = 1

We do not need to adjust for overlap since 13 is not an even number.

5. **Calculate the total favorable outcomes.**
So, we have:
\[
\text{Total favorable outcomes} = \text{Number of even balls} + \text{Number of 13} = 10 + 1 = 11
\]

6. **Calculate the probability.**
The probability \( P \) of selecting an even numbered ball or the number 13 is given by the ratio of the number of favorable outcomes to the total number of outcomes:
\[
P = \frac{\text{Total favorable outcomes}}{\text{Total outcomes}} = \frac{11}{21}
\]

Thus, the probability of selecting an even numbered ball or a 13 is \( \frac{11}{21} \).