Exam 8: Sets and Probability

Find the probability. -A basketball player hits her shot $42 \%$ of the time. If she takes four shots during a game, what is the probability that she hits all four? Express the answer as a percentage, and round to the nearest tenth (if necessary).

Insert " $\subseteq$ " or "q" in the blank to make the statement true. - $\{7,21,26\} \_\{16,21,26,36\}$

Suppose P(C) = .048, P(M ꓵ C) = .044, and P(M ꓴ C) = .524. Find the indicated probability. - $P\left(C^{\prime}\right)$

Use a Venn diagram to answer the question. -A local television station sends out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 900 responses with the following results: 270 were interested in an interview show and a documentary, but not reruns; 36 were interested in an interview show and reruns, but not a documentary; 126 were interested in reruns but not an interview show; 216 were interested in an interview show but not a documentary; 90 were interested in a documentary and reruns; 54 were interested in an interview show and reruns; 72 were interested in none of the three. How many are interested in exactly one kind of show?

For the experiment described, write the indicated event in set notation. -A die is tossed twice with the tosses recorded as an ordered pair. Represent the following event as a subset of the sample space: Both tosses show an even number.

Shade the Venn diagram to represent the set. - $\left(A \cap B \cap C^{\prime}\right)^{\prime}$

Find the complement of the set. - $\{x \mid x$ is an integer strictly between 0 and 9 $\}$ if $U$ is the set of all integers

For the experiment described, write the indicated event in set notation. -A die is tossed twice with the tosses recorded as an ordered pair. Represent the following event as a subset of the sample space: The sum of the tosses is five.

Find the complement of the set. - $\{x \mid x$ is a whole number less than 6 $\}$ if $U$ is the set of all whole numbers

Assume that, at a certain college, $33 \%$ of all physics majors belong to ethnic minorities. Given a random sample of 10physics majors, find the probability of the indicated event. Round your answer as appropriate. -Exactly 4 do not belong to an ethnic minority.

Insert " $\subseteq$ " or "q" in the blank to make the statement true. - $\{x \mid x$ is a counting number larger than 5 $\} \_\{7,8,9, \ldots\}$

Decide whether the statement is true or false. - $\{0\} \cap \varnothing=\{0\}$

Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability of the indicated result. -One marble is white, and one marble is blue.

Use a Venn diagram to decide if the statement is true or false. - $\mathrm{A} \cup(\mathrm{B} \cap \mathrm{C})^{\prime}=\left(\mathrm{A} \cup \mathrm{B}^{\prime}\right) \cap\left(\mathrm{A} \cup \mathrm{C}^{\prime}\right)$

Determine whether the given events are disjoint. -Being a male and being a nurse

Let $\mathrm{U}$ be the smallest possible universal set that includes all of the crops listed; and let $\mathrm{A}, \mathrm{K}$ , and $\mathrm{L}$ be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set. - $A \cap K$

An experiment is conducted for which the sample space is $S$ assignment ispossible for this experiment. -

Write the sample space for the given experiment. -A box contains 13 white cards numbered 1 through 13. One card with a number greater than 6 is chosen.

Let $U=\{q, r, s, t, u, v, w, x, y, z\} ; A=\{q, s, u, w, y\} ; B=\{q, s, y, z\} ;$ and $C=\{v, w, x, y, z\}$ . List the members of the indicated set, using set braces. - $\mathrm{A}^{\prime} \cup \mathrm{B}$

Decide whether the statement is true or false. - $\{3,5,7\} \cap\{4,6,8\}=\{3,5,7,4,6,8\}$