Question

Read and solve the problem; choose thebest answer(s) from the choices provided.You are hungry after school and walkacross the street to Bruster's. You plan topurchase a sundae. You have a choice ofa cup, sugar cone, or waffle cone. Icecream choices are limited to chocolateand vanilla. Topping choices aresprinkles, hot fudge, and crushedcookies. You are limited to one choice percategory.MAMD.M.D.1A: If you order a wafflecone sundae with vanilla ice cream andsprinkles, what is the probability that thenext person in line orders the exact samesundae?

Answer 1

You have to calculate the probability that the person after you orders a waffle cone sundae with vanilla ice cream and sprinkles.

Assuming that all choices are equally possible:

You have 3 cup choices: Cup(C), Sugar cone(S), or Waffle cone (W), the probability of choosing a waffle cone can be determined as follows:

`\begin{gathered} P(W)=\frac{nº\text{favorable outcomes}}{total\text{ outcomes}} \\ P(W)=(1)/(3) \end{gathered}`

There are two choices of ice cream: Vanilla (V), or Chocolate (C), the probability of choosing vanilla ice cream can be determined as follows:

`\begin{gathered} P(V)=\frac{nº\text{favorable outcomes}}{total\text{ outcomes}} \\ P(V)=(1)/(2) \end{gathered}`

And there are three topping choices: Sprinkles (S), Hot Fudge (F), or Crushed cookies (C), the probability of choosing sprinkles can be determined as follows:

`\begin{gathered} P(S)=\frac{nº\text{favorable outcomes}}{total\text{ outcomes}} \\ P(S)=(1)/(3) \end{gathered}`

All options are independent, which means that the probability of choosing "waffle come and vanilla ice cream and sprinkles" is equal to the product of the individual probabilities of each choice:

`P(W\cap V\cap S)=P(W)\cdot P(V)\cdot P(S)=(1)/(3)\cdot(1)/(2)\cdot(1)/(3)=(1)/(18)`

The probability is 1/18.