Question

question 1 of 25
an english teacher has equal numbers of fiction,
nonfiction, and poetry books. each day, she randomly
selects one book to read from. she designs a simulation to
estimate the probability that the next three books she
selects are all fiction.
which simulation design could she use to estimate the
probability?
a. random digits from 0 to 9
let 1, 2, 3 = fiction
let 4, 5, 6 = nonfiction
let 7, 8, 9, 0 = poetry
select three random digits from 0 to 9. repeat.
b. number cube
let 1, 3 = fiction
let 2, 4 = nonfiction
let 5, 6 = poetry
roll the cube three times. repeat.
c. number cube
let even number = fiction
let odd number = not fiction
roll the cube three times. repeat.
d. coin
let heads (h) = fiction
let tails (t) = nonfiction or poetry
toss the coin three times. repeat.

Explanation:

Step1: Analyze Option A

In option A, there are 10 digits (0 - 9). The number of digits assigned to fiction (\(1,2,3\)) is 3, to non - fiction (\(4,5,6\)) is 3, and to poetry (\(7,8,9,0\)) is 4. The probabilities of selecting fiction, non - fiction, and poetry are not equal.

Step2: Analyze Option B

A number cube has 6 faces. In option B, the number of outcomes assigned to fiction (\(1,3\)) is 2, to non - fiction (\(2,4\)) is 2, and to poetry (\(5,6\)) is 2. The probability of getting fiction \(P(\text{fiction})=\frac{2}{6}=\frac{1}{3}\), the probability of getting non - fiction \(P(\text{non - fiction})=\frac{2}{6}=\frac{1}{3}\), and the probability of getting poetry \(P(\text{poetry})=\frac{2}{6}=\frac{1}{3}\).

Step3: Analyze Option C

A number cube has 6 faces. The number of even numbers (assigned to fiction) is 3 (\(2,4,6\)), and the number of odd numbers (assigned to non - fiction or poetry) is 3 (\(1,3,5\)). But this only differentiates between fiction and non - fiction/poetry, not among fiction, non - fiction, and poetry.

Step4: Analyze Option D

A coin has 2 faces. The probability of getting heads (\(P(H)=\frac{1}{2}\)) and tails (\(P(T)=\frac{1}{2}\)). This does not account for three equal - probability categories (fiction, non - fiction, poetry).

Answer:

B. Number cube
Let \(1,3=\) fiction
Let \(2,4=\) nonfiction
Let \(5,6=\) poetry
Roll the cube three times. Repeat.