You are handed 5 pieces of silverware for the formal setting shown. If you guess their placement at random, what is the probability that the knife and spoon are placed correctly?

Use the formal definitions of limit as $x \rightarrow \pm \infty$ to establish the limit in this exercise.

If $f$ has the constant value $f(x)=k$, then $\lim _{x \rightarrow-\infty} f(x)=k$.

The probability of randomly selecting a knife, a fork, and a spoon in that order from a kitchen drawer containing 8 spoons, 8 forks, and 12 table knives.

The standings list after the first day of a 3-day tournament is shown below. What is the probability that Wyatt, Gabe, and Isaac will all finish in the top 3 ?

Tory and Emilio's motorboats travel at the same speed. Tory pilots her boat $40 \mathrm{~km}$ before docking. Emilio continues for another $2 \mathrm{~hr}$, traveling a total of $100 \mathrm{~km}$ before docking. How long did it take Tory to navigate the $40 \mathrm{~km}$?

In this exercise, find a polynomial function

$$f(x)=a_n x^n+a_{n-1} x^{n-1}+\cdots+a_2 x^2+a_1 x+a_0$$

that has only the specified extrema. Using the fact that the coordinates of the extrema are solution points of the function, and that the $x$-coordinates are critical numbers, determine a system of linear equations whose solution yields the coefficients of the required function.

Relative minimum: $(1,2)$ Relative maxima: $(-1,4),(3,4)$

Kali has a choice of 20 flavors for her triple scoop cone. What is the chance that she will pick vanilla, chocolate, and strawberry out of the three tastes if she chooses them at random?

Alfonso and Colin each bought one raffle ticket at the state fair. If 50 tickets were randomly sold, what is the probability that Alfonso got ticket 14 and Colin got ticket 23?

The cheerleading squad is made up of 12 girls. Random selection is used to choose the captain and co-captain. How likely is it that Chantel and Clover will be picked as the leaders?

Draw tree diagrams for the following situations. Determine whether the events are independent or not.

The probability that Pete plays video games given that it is Saturday is $75 \%$. On any other day of the week, the probability is $\frac{3}{4}$. Let $B$ be the event "playing video games" and $A$ be the event "the day is Saturday."

Explain how the multiplication property of probability diagrams is used to determine the probabilities of events for the tree in part a.

How do tree diagrams, tables, and lists help you find the probability of a compound event?

After an introductory statistics course, 78 % of students can successfully construct tree diagrams. Of those who can construct tree diagrams, $97 \%$ passed, while only $57 \%$ of those students who could not construct tree diagrams passed. (a) Organize this information into a tree diagram. (b) What is the probability that a randomly selected student passed? (c) Compute the probability a student is able to construct a tree diagram if it is known that she passed.

Draw probability tree diagrams for the following experiments.

Spinner A spun, then spinner B spun [Hint: Draw a two-stage tree combining results of parts a and b.]