Question

select the correct answer. mark, anthony, and derek, are going on a road trip and will take turns driving the car. they need to decide who will drive first. which method assures that each of the three friends has a fair chance of being selected to drive first? a. roll an ordinary die. if the die lands on 1 or 4, mark drives first. if the die lands on 2 or 5, anthony drives first. if the die lands on 3 or 6, derek drives first. b. flip two fair coins. if both coins land on tails, mark drives first. if both coins land on heads, anthony drives first. if one coin lands on tails and the other lands on heads, derek drives first. c. using a random number generator, generate an integer. if the number is negative, mark drives first. if the number is positive, anthony drives first. if the number is 0, derek drives first. d. spin a spinner with four equal - sized sections labeled a, b, c, and d. if the spinner lands on a, mark drives first. if the spinner lands on b, anthony drives first. if the spinner lands on c, derek drives first. if the spinner lands on d, mark drives first.

Explanation:

Step1: Calculate probabilities for option A

An ordinary die has 6 sides. For Mark, the probability of getting 1 or 4 is $\frac{2}{6}=\frac{1}{3}$. For Anthony, the probability of getting 2 or 5 is $\frac{2}{6}=\frac{1}{3}$. For Derek, the probability of getting 3 or 6 is $\frac{2}{6}=\frac{1}{3}$.

Step2: Calculate probabilities for option B

When flipping two fair coins, there are $2\times2 = 4$ possible outcomes: (HH), (HT), (TH), (TT). The probability that both coins land on tails (Mark drives first) is $\frac{1}{4}$. The probability that both coins land on heads (Anthony drives first) is $\frac{1}{4}$. The probability that one coin lands on tails and the other on heads (Derek drives first) is $\frac{2}{4}=\frac{1}{2}$. So it's not fair.

Step3: Calculate probabilities for option C

When using a random - number generator to generate an integer, the probability of getting a negative number, a positive number, and 0 is not necessarily $\frac{1}{3}$ each. In the set of all integers, the number of negative and positive integers is infinite and the concept of probability in this non - finite set is not well - defined as $\frac{1}{3}$ for each case. So it's not fair.

Step4: Calculate probabilities for option D

A spinner with 4 equal - sized sections: The probability that Mark drives first (lands on A or D) is $\frac{2}{4}=\frac{1}{2}$, the probability that Anthony drives first (lands on B) is $\frac{1}{4}$, and the probability that Derek drives first (lands on C) is $\frac{1}{4}$. So it's not fair.

Answer:

A. Roll an ordinary die. If the die lands on 1 or 4, Mark drives first. If the die lands on 2 or 5, Anthony drives first. If the die lands on 3 or 6, Derek drives first.