Question

question 24 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. 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.
b. roll a number cube. if it lands on 1 or 2, alina wins. if it lands on 3
or 5, robert wins. if it lands on any other number, makayla wins.
c. roll a number cube. if the number is odd, alina wins. if the
number is even, robert wins. if its any other number, makayla
wins.
d. write each students name on a slip of paper and put the slips in a
hat. randomly draw a slip of paper. the student whose name is
on the paper wins.

Explanation:

Step1: Check fairness of Option A

Two coin flips have 4 outcomes: HH, HT, TH, TT. Alina (HH): 1/4, Makayla (TT):1/4, Robert (HT/TH):2/4=1/2. Unequal probabilities → unfair.

Step2: Check fairness of Option B

Number cube has 6 faces. Alina (1,2):2/6=1/3, Robert (3,5):2/6=1/3, Makayla (4,6):2/6=1/3. Equal probabilities → fair.

Step3: Check fairness of Option C

Number cube: odd (1,3,5)=3 faces, even (2,4,6)=3 faces. No "other number" → Makayla has 0 probability → unfair.

Step4: Check fairness of Option D

3 slips, each has 1/3 chance of being drawn. Equal probabilities → fair.

Answer:

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