Question

Students at Freeman Middle School have a choice of water, milk, or juice for breakfast. From a survey, it was determined that 50 students prefer water, 100 prefer juice, and 150 prefer milk. You want to know the probability that exactly three of four randomly selected students do not prefer water. How could you model this scenario? This scenario can be simulated by rolling a six-sided die __ times.

A. 3
B. 4
C. 5
D. 6
E. 7

Answer 1

To simulate the probability that exactly three of four students do not prefer water, a six-sided die should be rolled 4 times, with the sides assigned to represent the beverage preferences proportionally.

Step-by-step explanation:

To model the scenario of finding the probability that exactly three of four randomly selected students do not prefer water, we can use a six-sided die to represent the preferences of students. Since there are 50 students who prefer water, 100 who prefer juice, and 150 who prefer milk, we can assign numbers to the die such that 1 and 2 represent water (50 out of 300 total preferences, or 1/3 of the die), 3 and 4 represent juice (100 out of 300 preferences, or 1/3 of the die), and 5 and 6 represent milk (150 out of 300 preferences, or the remaining 1/3 of the die).

We would roll the die four times to represent the four randomly selected students. Each roll corresponds to a student's beverage preference. We are looking for the number of times (out of four) that the outcome is not 1 or 2, which corresponds to students not preferring water. Since we're interested in the outcome for each of four students, the correct answer is B. 4 times to simulate this scenario with a six-sided die.