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:
-
Identify the total number of balls.
There are 21 balls in total (numbered 1 through 21). -
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. -
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. -
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.
-
Calculate the total favorable outcomes.
So, we have: \[ \text{Total favorable outcomes} = \text{Number of even balls} + \text{Number of 13} = 10 + 1 = 11 \] -
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 \( \frac{11}{21} \).
1 answer