Exam 8: Sets and Probability

Solve the problem. -A survey revealed that $31 \%$ of people are entertained by reading books, $37 \%$ are entertained by watching TV, and $15 \%$ are entertained by both books and TV. What is the probability that a person will be entertained by either books or TV? Express the answer as a percentage.

Write the sample space for the given experiment. -A box contains 3 blue cards numbered 1 through 3 , and 4 green cards numbered 1 through 4 . A blue card is picked, followed by a green card.

Solve the problem. -If two fair dice are rolled, find the probability that the roll is a double given that the sum is 11 .

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

Tell whether the statement is true or false. - $13 \notin\{x \mid x$ is an even counting number $\}$

Shade the Venn diagram to represent the set. - $\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}$

Find the probability. -A family has five children. The probability of having a girl is $\frac{1}{2}$ . What is the probability of having at least 4 girls? Round the answer to the fourth decimal place.

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

Insert " $\subseteq$ " or "q" in the blank to make the statement true. - $\{1,3,5\} \_\{x \mid x \text { is an odd counting number }\}$

Use a Venn diagram to answer the question. -At East Zone University (EZU) there are 688 students taking College Algebra or Calculus. 495 are taking College Algebra, 210 are taking Calculus, and 17 are taking both College Algebra and Calculus. How many are taking Calculus but not Algebra?

Find the probability. -A family has five children. The probability of having a girl is $\frac{1}{2}$ . What is the probability of having 2 girls followed by 3 boys? Round the answer to the fourth decimal place.

Determine whether the given events are disjoint. -Drawing a spade from a deck of cards and drawing an ace

A die is rolled twice. Write the indicated event in set notation. -The sum of the rolls is 8.

Decide whether the statement is true or false. - $\{2,13,12\} \cup\{12,2,13\}=\{2,12\}$

Solve the problem. -Of the coffee makers sold in an appliance store, $5.0 \%$ have either a faulty switch or a defective cord, $1.1 \%$ have a faulty switch, and $0.9 \%$ have both defects. What is the probability that a coffee maker will have a defective cord? Express the answer as a percentage.

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. - $\mathrm{K} \cup \mathrm{L}$

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. - $\$ 35,000$ - $\$ 39,999$

Solve the problem using Bayes' Theorem. Round the answer to the nearest hundredth, if necessary. -For mutually exclusive events $X_{1}, X_{2}$ , and $X_{3}$ , let $P\left(X_{1}\right)=.32, P\left(X_{2}\right)=.40$ , and $P\left(X_{3}\right)=.28$ . Also, $\mathrm{P}\left(\mathrm{Y} \mid \mathrm{X}_{1}\right)=.40, \mathrm{P}\left(\mathrm{Y} \mid \mathrm{X}_{2}\right)=.30$ and $\mathrm{P}\left(\mathrm{Y} \mid \mathrm{X}_{3}\right)=.60$ . Find $\mathrm{P}\left(\mathrm{X}_{3} \mid \mathrm{Y}\right)$ .

Find the probability. -In a certain city, $14 \%$ of the people are business executives, and $29 \%$ of the business executives drive Cadillacs. Assuming independent events, what is the probability of choosing a business executive who drives a Cadillac? Round the answer to the nearest hundredth.

For the experiment described, write the indicated event in set notation. -From six job applicants, two people are selected for an interview. The names of the applicants are Ruth, Kim, Nancy, Jeff, Mark, and Lisa. Represent the event "Lisa is selected" as a subset of the sample space.