Three people have been exposed to a certain illness. Once exposed, a person has a 50–50 chance of actually becoming ill. a. What is the probability that exactly one of the people becomes ill? b. What is the probability that at least two of the people becomes ill? c. What is the probability that none of the three people becomes ill?

In a competition between players X and Y, the first player to win three games in a row or a total of four games wins. How many ways can the competition be played if X wins the first game and Y wins the second and third games? (Draw a tree.)

Suppose that on a true/false exam you have no idea at all about the answers to three questions. You choose answers randomly and therefore have a 50–50 chance of being correct on any one question. Let CCW indicate that you were correct on the first two questions and wrong on the third, let WCW indicate that you were wrong on the first and third questions and correct on the second, and so forth. a. List the elements in the sample space whose outcomes are all possible sequences of correct and incorrect responses on your part. b. Write each of the following events as a set and find its probability: (i) The event that exactly one answer is correct. (ii) The event that at least two answers are correct. (iii) The event that no answer is correct.

a. How many integers are there from 1000 through 9999? b. How many odd integers are there from 1000 through 9999? c. How many integers from 1000 through 9999 have distinct digits? d. How many odd integers from 1000 through 9999 have distinct digits? e. What is the probability that a randomly chosen fourdigit integer has distinct digits? has distinct digits and is odd?

If the largest of 56 consecutive integers is 279, what is the smallest?

On a separate sheet of paper, explain the following term by using it correctly in a sentence. arboreal

A major cyanobacteria food source used in many parts of the world is _________.

Find the function whose tangent line has slope $x e^{-2 x^{2}}$ for each x and whose graph passes through the point (0, -3).

Which of the common food allergens must be identified on ingredient labels?

a. Carrots

b. Potatoes

c. Nuts

d. Rice

a. How many positive three-digit integers are multiples of 6. b. What is the probability that a randomly chosen positive three-digit integer is a multiple of 6? c. What is the probability that a randomly chosen positive three-digit integer is a multiple of 7?

A person buying a personal computer system is offered a choice of three models of the basic unit, two models of keyboard, and two models of printer. How many distinct systems can be purchased?

A food worker has finished cutting raw chicken on a cutting board.

What must he do before using this cutting board to slice potatoes?

a. Peel the potatoes

b. Sanitize his hands

c. Clean and sanitize the cutting board

d. Scrape off any remaining chicken

Translate into English and indicate whether the sentence contains a perfect passive verb or a perfect passive participle: Hostes in proelio captos videre non potuimus.

Match each term associated with a bank reconciliation with its description.

$$\begin{matrix} \text{Terms} & \text{Descriptions}\\ \hline \text{\_\_\_\_\_ 1. Checks outstanding} & \text{a. Cash receipts received by the company but not yet recorded by the bank.}\\ \text{\_\_\_\_\_ 2. NSF checks} & \text{b. Fees imposed by the bank to the company for providing routine services.}\\ \text{\_\_\_\_\_ 3. Company error} & \text{c. Checks written to the company that are returned by the bank as not having adequate funds.}\\ \text{\_\_\_\_\_ 4. Interest earned} & \text{d. Checks written by the company but not yet recorded by the bank.}\\ \text{\_\_\_\_\_ 5. Deposits outstanding} & \text{e. Money earned on the average daily balance of the checking account.}\\ \text{\_\_\_\_\_ 6. Bank service fees} & \text{f. The company recorded a deposit twice.}\\ \end{matrix}$$