2014 CEMC Gauss (Grade 8) Problems/Problem 14

Problem

Betty is making a sundae. She must randomly choose one flavour of ice cream (chocolate or vanilla or strawberry), one syrup (butterscotch or fudge) and one topping (cherry or banana or pineapple). What is the probability that she will choose a sundae with vanilla ice cream, fudge syrup and banana topping?

$\text{ (A) }\ \frac{1}{18} \qquad\text{ (B) }\ \frac{1}{6} \qquad\text{ (C) }\ \frac{1}{8} \qquad\text{ (D) }\ \frac{1}{9} \qquad\text{ (E) }\ \frac{1}{12}$

Solution

We can use the fact that the probability will be the number of outcomes that match the description divided by the total number of possibilities.

First, we can see that there are $3$ flavors, $2$ syrups, and $3$ toppings. Thus, the total number of possibilities is $3 \times 2 \times 3 = 6 \times 3 = 18$ .

We also can see that there is only $1$ way for the sundae to have vanilla ice cream, fudge syrup, and banana as the topping all at the same time.

Using these two facts, the probability of choosing such a sundae is $\boxed {\textbf {(A) } \frac{1}{18}}$ .

~anabel.disher

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2014 CEMC Gauss (Grade 8) Problems/Problem 14

Problem

Solution