To find the probability that Ellie chooses a number less than 3 from a range of 1 to 10, let’s follow these steps:
1. Determine the Total Number of Possible Outcomes:
Since Ellie can choose any number from 1 to 10, there are 10 possible outcomes. These outcomes are the numbers {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
2. Identify the Favorable Outcomes:
We need to find the numbers less than 3. The numbers in the range from 1 to 10 that are less than 3 are {1, 2}. Thus, there are 2 favorable outcomes.
3. Calculate the Probability:
The probability is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
[tex]\[
\text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} = \frac{2}{10}
\][/tex]
4. Simplify the Fraction:
Simplifying the fraction [tex]\(\frac{2}{10}\)[/tex] gives:
[tex]\[
\frac{2}{10} = \frac{1}{5}
\][/tex]
5. Identify the Correct Option:
Looking at the provided options:
- A. [tex]\(\frac{3}{10}\)[/tex]
- B. [tex]\(\frac{1}{5}\)[/tex]
- C. [tex]\(\frac{2}{9}\)[/tex]
- D. [tex]\(\frac{4}{5}\)[/tex]
The simplified probability [tex]\(\frac{1}{5}\)[/tex] matches option B.
Therefore, the correct option is B.
