Answered

Alex asked his 40 classmates of
their favorite snacks. These are the
responses of his classmates;
10 students chose banana cue; 12 chose
cassava cake and 18 chose pancakes. If
one of his classmates is chosen at
random, what is the probability that the
chosen classmate prefers cassava cake?

Verified Answer :

GinnyAnswer

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:
\(\[ P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]\)
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:
\(\[ P(\text{Cassava Cake}) = \frac{12}{40} \]\)

5. Simplifying the Fraction:
To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 4:
\(\[ \frac{12 \div 4}{40 \div 4} = \frac{3}{10} \]\)

6. Result:
Therefore, the probability that a randomly chosen classmate prefers cassava cake is:
\(\[ \frac{3}{10} \]\)

In conclusion, the probability that a randomly selected classmate prefers cassava cake is \(\(\frac{3}{10}\)\).

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