Question

Charity is ordering a sundae at a restaurant, and the server tells her that she can have up to five toppings: chocolate chips, butterscotch sauce, strawberries, a cherry, and hot fudge. Since she cannot decide how many of the toppings she wants, she tells the server to surprise her. If the server randomly chooses which toppings to add, what is the probability that Charity gets just chocolate chips and a cherry? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

1/31 = 0.0323 probability that Charity gets just chocolate chips and a cherry.

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Number of subsets in a set of n elements:

The number of subsets in a set of n elements, including the empty set, is given by:

`2^(n)`

Up to five toppings:

Up to five toppings means that the total number of possibilities is:

`T = 2^(5) - 1 = 32 - 1 = 31`

We subtract one to disconsider the option with no toppings.

What is the probability that Charity gets just chocolate chips and a cherry?

Chocolate chips and cherry is 1 subset, so
`D = 1`

The probability is:

`p = (D)/(T) = (1)/(31) = 0.0323`

1/31 = 0.0323 probability that Charity gets just chocolate chips and a cherry.