Question

question 3 of 25.
alina, robert, and makayla are on the student council at their high school. they all want to go to a dinner where student council representatives from other schools will participate. however, only one student per school can go. how can a fair decision be made about who goes to the dinner?
select all that apply.

a. roll a number cube. if it lands on 1 or 3, alina wins. if it lands on 2 or 4, robert wins. if it lands on 5 or 6, makayla wins.
b. roll a number cube. if the number is even, alina wins. if the number is 1 or 3, robert wins. if its any other number, makayla wins.
c. flip a coin twice. if both tosses are heads, alina wins. if both are tails, makayla wins. if one is heads and one is tails, robert wins.
d. write each students name on a slip of paper and put the slips in a bag. randomly draw a slip of paper. the student whose name is on the paper wins.

Explanation:

Step1: Calculate probability for option A

A number cube has 6 faces. For Alina: \(P(\text{Alina})=\frac{2}{6}=\frac{1}{3}\). For Robert: \(P(\text{Robert})=\frac{2}{6}=\frac{1}{3}\). For Makayla: \(P(\text{Makayla})=\frac{2}{6}=\frac{1}{3}\).

Step2: Calculate probability for option B

Even numbers on a cube (2,4,6): \(P(\text{Alina})=\frac{3}{6}=\frac{1}{2}\). For Robert (1,3): \(P(\text{Robert})=\frac{2}{6}=\frac{1}{3}\). For Makayla (5): \(P(\text{Makayla})=\frac{1}{6}\). Probabilities are not equal.

Step3: Calculate probability for option C

Flip a coin twice. Total outcomes \(n(S) = 2\times2=4\) (HH, HT, TH, TT). For Alina (\(HH\)): \(P(\text{Alina})=\frac{1}{4}\). For Makayla (\(TT\)): \(P(\text{Makayla})=\frac{1}{4}\). For Robert (\(HT,TH\)): \(P(\text{Robert})=\frac{2}{4}=\frac{1}{2}\). Probabilities are not equal.

Step4: Calculate probability for option D

There are 3 slips. \(P(\text{each student})=\frac{1}{3}\)

Answer:

A. Roll a number cube. If it lands on 1 or 3, Alina wins. If it lands on 2 or 4, Robert wins. If it lands on 5 or 6, Makayla wins.
D. Write each student's name on a slip of paper and put the slips in a bag. Randomly draw a slip of paper. The student whose name is on the paper wins.