To determine the probability that Dunya chooses a number less than 6 from the numbers 1 to 10, we can follow these steps:
1. Identify the Total Number of Possible Outcomes:
The numbers from which Dunya can choose are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. This totals to 10 numbers.
2. Identify the Number of Favorable Outcomes:
We want to find how many numbers are less than 6. These numbers are 1, 2, 3, 4, and 5. Therefore, there are 5 favorable outcomes.
3. Calculate the Probability:
The probability [tex]\( P \)[/tex] of choosing a number less than 6 is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
[tex]\[
P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} = \frac{5}{10}
\][/tex]
4. Simplify the Fraction:
The fraction [tex]\(\frac{5}{10}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 5.
[tex]\[
\frac{5}{10} = \frac{1}{2}
\][/tex]
So, the probability that Dunya chooses a number less than 6 is [tex]\(\frac{1}{2}\)[/tex].
Therefore, the correct answer is:
C. [tex]\(\frac{1}{2}\)[/tex]
