To determine the probability that a randomly chosen classmate prefers cassava cake, we follow a simple process involving counting and probability concepts.
1. Total Number of Classmates:
Alex has asked 40 classmates about their favorite snacks.
2. Number of Classmates Preferring Cassava Cake:
Out of these 40 classmates, 12 said their favorite snack is cassava cake.
3. Probability Formula:
Probability can be calculated using the formula:
[tex]\[
P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\][/tex]
In this scenario:
- The "favorable outcomes" are the classmates who prefer cassava cake.
- The "total possible outcomes" are all of Alex's classmates.
4. Calculation:
- The number of favorable outcomes for cassava cake = 12
- The total number of possible outcomes (total classmates) = 40
Plug these values into the probability formula:
[tex]\[
P(\text{Cassava Cake}) = \frac{12}{40}
\][/tex]
5. Simplifying the Fraction:
To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 4:
[tex]\[
\frac{12 \div 4}{40 \div 4} = \frac{3}{10}
\][/tex]
6. Result:
Therefore, the probability that a randomly chosen classmate prefers cassava cake is:
[tex]\[
\frac{3}{10}
\][/tex]
In conclusion, the probability that a randomly selected classmate prefers cassava cake is [tex]\(\frac{3}{10}\)[/tex].
