To find the probability that someone gets vanilla in a bowl, let’s analyze the problem step-by-step.
Firstly, we need to determine the total number of possible choices. Each student has three dimensions of choice:
1. The number of scoops: 1 scoop or 2 scoops (2 choices).
2. The flavor: chocolate or vanilla (2 choices).
3. The container: in a cup or in a bowl (2 choices).
To find the total number of choices, we multiply the number of options in each dimension:
[tex]\[ \text{Total number of choices} = 2 \text{ (scoops)} \times 2 \text{ (flavors)} \times 2 \text{ (containers)} = 8 \][/tex]
Now, we need to determine the number of favorable outcomes where students get vanilla in a bowl. Let's break it down:
1. The number of scoops: 1 scoop or 2 scoops (2 choices).
2. The flavor: vanilla (1 choice).
3. The container: in a bowl (1 choice).
So, the number of favorable outcomes is:
[tex]\[ \text{Number of favorable outcomes} = 2 \text{ (scoops)} \times 1 \text{ (flavor: vanilla)} \times 1 \text{ (container: bowl)} = 2 \][/tex]
Now, to find the probability, we divide the number of favorable outcomes by the total number of choices:
[tex]\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of choices}} = \frac{2}{8} = \frac{1}{4} \][/tex]
Thus, the probability that someone gets vanilla in a bowl is:
[tex]\[ \boxed{\frac{1}{4}} \][/tex]
