Question

At the Royal Dragon Chinese restaurant, a slip in the fortune cookies indicates a dollar amount that will be subtracted from your total bill. A bag of 10 fortune cookies is given to you from which you will select one. If five fortune cookies contain "$1off." four contain "$2 off." and one contains "$5 off." determine the expectation of a selection.

Answer 1

ANSWER:

$1.8

EXPLANATION:

Given:

A bag of 10 fortune cookies;

Five fortune cookies contain "$1 off"

Four contain "$2 off"

One contains "$5 off"

So the probability of selecting a "$1 off" cookie will be;

$\begin{gathered} P(\text{\ 1 }off\text{ }cookie)=\frac{5}{10} \\ =\frac{1}{2} \end{gathered}$

And the probability of selecting a "$2 off" cookie will be;

$\begin{gathered} P(\text{\ 2 }off\text{ }cookie)=\frac{4}{10} \\ =\frac{2}{5} \end{gathered}$

the probability of selecting a "$5 off" cookie will be;

$\begin{gathered} P(\text{\ 5 }off\text{ }cookie)=\frac{1}{10} \\ \end{gathered}$

We can determine the expectation of a selection as seen below;

$\begin{gathered} Expectation=(1*\frac{1}{2})+(2*\frac{2}{5})+(5*\frac{1}{10}) \\ \\ =\frac{1}{2}+\frac{4}{5}+\frac{1}{2} \\ \\ =\frac{9}{5} \\ \\ =\text{ \ }1.8\text{ }off \end{gathered}$

So the expectation of a selection will be $1.8 off