Algebra 2

In the game Rock-Paper-Scissors, the scissors cut the paper, the rock dulls the scissors, and the paper covers the rock. Use the results below for Exercises 1 and 2.
Rock-Paper-Scissors
Table cannot copy
$\mathrm{R}=\mathrm{Rock} \quad \mathrm{P}=$ Paper $\quad \mathrm{S}=$ Scissors $\quad$ Bold $=$ Winner
Make a frequency table for the objects played: rock, paper, or scissors.

In the game Rock-Paper-Scissors, the scissors cut the paper, the rock dulls the scissors, and the paper covers the rock. Use the results below for Exercises 1 and 2.
Rock-Paper-Scissors
Table cannot copy
$\mathrm{R}=\mathrm{Rock} \quad \mathrm{P}=$ Paper $\quad \mathrm{S}=$ Scissors $\quad$ Bold $=$ Winner
Make a frequency table for the winning players: Player $1,$ Player $2,$ or tie.

The table shows the frequency of responses to editorials. Find each probability.
$$
\begin{array}{|l|l|l|l|l|l|l|}\hline \text { Number of Responses } & {0} & {1} & {2} & {3} & {4} & {5} & {6 \text { or more }} & {\text { Total }} \\ \hline \text { Number of Editorials } & {20} & {30} & {56} & {38} & {34} & {16} & {6} & {200} \\ \hline\end{array}
$$
$P(5 \text { or more responses })$

The table shows the frequency of responses to editorials. Find each probability.
$$
\begin{array}{|l|l|l|l|l|l|l|}\hline \text { Number of Responses } & {0} & {1} & {2} & {3} & {4} & {5} & {6 \text { or more }} & {\text { Total }} \\ \hline \text { Number of Editorials } & {20} & {30} & {56} & {38} & {34} & {16} & {6} & {200} \\ \hline\end{array}
$$
$P(\text { at most } 4 \text { responses })$

The table shows the frequency of responses to editorials. Find each probability.
$$
\begin{array}{|l|l|l|l|l|l|l|}\hline \text { Number of Responses } & {0} & {1} & {2} & {3} & {4} & {5} & {6 \text { or more }} & {\text { Total }} \\ \hline \text { Number of Editorials } & {20} & {30} & {56} & {38} & {34} & {16} & {6} & {200} \\ \hline\end{array}
$$
$P(0-2 \text { responses })$

Use a table and a graph to show the probability distribution for the spinner {red, green, blue, yellow $}.

Use a table and a graph to show the probability distribution for the number of days $\{28,29,30,31\}$ in each of 48 consecutive months.

Suppose you roll two number cubes. Graph the probability distribution for each sample space.
{sum of numbers even, sum of numbers odd}

Suppose you roll two number cubes. Graph the probability distribution for each sample space.
{both numbers even, both numbers odd, one number even and the other odd}

Suppose you roll two number cubes. Graph the probability distribution for each sample space.
Design and conduct a simulation to determine the ages of 20 licensed drivers chosen at random in the United States.

Design and conduct a simulation to determine the size and type of 30 cars purchased from U.S. car dealerships.

Graph the probability distribution described by each function.
$$
P(x)=\frac{x}{10} \text { for } x=1,2,3, \text { and } 4
$$

Graph the probability distribution described by each function.
$$
P(x)=\frac{2 x+1}{15} \text { for } x=1,2, \text { and } 3
$$

Weather. Refer to the table at the left.
a. Make a table showing the probability distribution for weather in Dayton.
b. Define the independent and dependent variables.
c. Find the probability that a day in Dayton will include rain or snow.

Data Collection. Find weather data for a city near you. Draw a graph to show the probability distribution of weather conditions.

a. Transportation Sometimes a probability distribution is shown as a circle graph. Define the independent and dependent variables in the distribution at the right.
b. Draw the distribution as a bar graph.
c. Find $P(\text { the tank is at least half full }$ when a driver buys gas).

Writing. In a simulation, how do equally likely outcomes help you represent the probability distribution?

Odds The odds in favor of an event equal the ratio of the number of times the event occurs to the number of times the event does not occur. The odds in favor of event $A$ are $1 : 4 .$ The odds in favor of event $B$ are $2 : 3 .$ The odds in favor of event C are $1 : 3 .$ The odds in favor of event $\mathrm{D}$ are $3 : 17 .$ Graph the probability distribution of events $\mathrm{A}, \mathrm{B}, \mathrm{C},$ and $\mathrm{D}$ .

Safety The table shows data for 911 calls in a town.
a. Conduct a simulation for the number of 911 calls over a 24 hour period.
b. If there are two response teams available, and each response takes about an hour, how many callers in your simulation have to wait?
c. Find $P(\text { caller will have to wait). }$
d. Critical Thinking Use your simulation to determine whether additional response teams are needed for this town. Explain your reasoning.

Marketing A company includes instant-win tickets with $10,000,000$ of its products. Of the prizes offered, one is a large cash prize, $1,600,000$ are small cash prizes, and the other prizes are free samples of the company's products.
a. Find the theoretical probability of winning each type of prize.
b. Design and conduct a simulation to determine the prizes for 100 products.
c. Find the experimental probability for winning each type of prize.

The table shows the number of cities in a region of the U.S. that are served by the given number of airlines. Use the table for Exercises $21-22$ .
What is the probability that a city chosen at random is served by exactly 4 airlines?
$$
\begin{array}{llll}{\text { A. } \frac{1}{18}} & {\text { B. } \frac{4}{21}} & {\text { C. } \frac{2}{11}} & {\text { D. } \frac{2}{9}}\end{array}
$$

The table shows the number of cities in a region of the U.S. that are served by the given number of airlines. Use the table for Exercises $21-22$ .
What is the probability that a city chosen at random is served by at least 1 airline?
$$
\begin{array}{llll}{\text { F. } 0} & {\text { G. } \frac{1}{99}} & {\text { H. } \frac{3}{11}} & {\text { J. } 1}\end{array}
$$

A spinner has 4 sections labeled $A, B, C,$ and $D .$ Can the spinner be designed so $P(A)=\frac{1}{12}, P(B)=\frac{1}{6}, P(C)=\frac{1}{3},$ and $P(D)=\frac{5}{12} ?$ If so, explain how.

Find the area under each curve for the domain $0 \leq x \leq 1$
$$
y=3
$$

Find the area under each curve for the domain $0 \leq x \leq 1$
$$
y=4 x+2
$$

Find the area under each curve for the domain $0 \leq x \leq 1$
$$
y=4 x^{3}+1
$$

Sketch the graph of each equation.
$$
x^{2}-4 y^{2}+2 x+24 y=51
$$

Sketch the graph of each equation.
$$
20 y^{2}-40 y-x=-25
$$

Classify each pair of events as dependent or independent.
Choose one item from a buffet. Then choose a different item from the buffet.

Classify each pair of events as dependent or independent.
Choose a size for your drink. Then select a flavor.