To determine the probability of randomly selecting a number less than 12 from a box containing cards numbered from 1 to 100, follow these steps:
1. Identify the total number of possible outcomes.
- Since the cards are numbered from 1 to 100, there are 100 possible outcomes.
2. Identify the number of favorable outcomes.
- The favorable outcomes are the numbers that are less than 12. These numbers are 1, 2, 3, ..., 11. Count these numbers to get the total:
[tex]\[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 \][/tex]
- There are 11 numbers in total that are less than 12.
3. Calculate the probability.
- The probability [tex]\( P \)[/tex] is given by the ratio of the number of favorable outcomes to the number of possible outcomes:
[tex]\[
P(\text{number less than 12}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{11}{100}
\][/tex]
Therefore, the probability of randomly selecting a number that is less than 12 is:
[tex]\[
\frac{11}{100}
\][/tex]
So, the correct answer is:
[tex]\(\frac{11}{100}\)[/tex]
