Exam 8: Sets and Probability

Solve the problem, rounding the answer as appropriate. Assume that "pure dominant" describes one who has twodominant genes for a given trait; "pure recessive" describes one who has two recessive genes for a given trait; and"hybrid" describes one who has one of each. -Suppose a hybrid mates with a pure dominant. If they produce two offspring, what is the probability that neither is a hybrid?

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. - $\mathrm{C}^{\prime} \cap \mathrm{A}^{\prime}$

Determine whether the given events are disjoint. -Being over 30 and being in college

The table shows, for some particular year, a listing of several income levels and, for each level, the proportion of the population in the level and the probability that a person in that level bought a new car during the year. Given that one of the people who bought a new car during that year is randomly selected, find the probability that that person was in the indicated income category. Round your answer to the nearest hundredth. - $\$ 5000-\$ 9999$

Write the sample space for the given experiment. -A lottery uses balls numbered 1 through 39. An even-numbered ball is picked.

A sample space $S$ is a set of 7 outcomes. What is the most distinct events that $S$ can have?

Decide whether the statement is true or false. - $\{8,14,15\} \cup \varnothing=\{8,14,15\}$

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. -B'

Decide whether the two events listed are independent. -Two cards are selected, without replacement, from an ordinary deck. F is the event that an ace appears on the first draw. $S$ is the event that an ace appears on the second draw.

Assume that $\mathrm{E}$ and $\mathrm{F}$ are events. Must the union of $\mathrm{E}$ and $\mathrm{F}$ also be an event? Must the intersection of $\mathrm{E}$ and $\mathrm{F}$ also be an event?

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

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

Write the sample space for the given experiment. -An ordinary die is rolled.

The table shows, for some particular year, a listing of several income levels and, for each level, the proportion of the population in the level and the probability that a person in that level bought a new car during the year. Given that one of the people who bought a new car during that year is randomly selected, find the probability that that person was in the indicated income category. Round your answer to the nearest hundredth. - $\$ 40,000$ - $\$ 49,999$

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

Solve the problem. -Below is a table of data from a high school survey given to 500 parents. Find the probability that a rand omly chosen parent would agree or strongly agree that the school is clean. Round your answer to the nearest hundred th.

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. - $\mathrm{K}^{\prime} \cap \mathrm{L}$

Solve the problem. -The given contingency table gives the number (in thousands) of U.S. households classified by educational attainment (high school graduate or less denoted with A, some college with no degree denoted B, an associate's degree denoted with C, and a bachelor's degree or higher denoted with D) and household income ($0 - $34,999 denoted with E, $35,000-$49,999 denoted with F,$50,000-$74,999 denoted G, and $75,000 and over denoted H). Find the number of households in the given set. $\mathrm{C} \cap \mathrm{F}^{\prime}$

Find the probability of the given event. -A bag contains 7 red marbles, 3 blue marbles, and 1 green marble. A randomly drawn marble is not blue.

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