Question

mrs. piper is driving anna, jo, and mai home from school. all of them want to ride in the front seat. how can she make a fair decision about who rides in the front seat? select all of the correct answers. a. put each persons name on a separate piece of paper in a bag. randomly draw the winning name. b. flip a coin twice. if both tosses are heads, anna wins. if both tosses are tails, jo wins. if one is heads and one is tails, mai wins. c. roll a number cube. if it lands on 1, anna wins. if it lands on 2, jo wins. if it lands on any other number, mai wins. d. roll a number cube. if it lands on 1 or 6, anna wins. if it lands on 2 or 5, jo wins. if it lands on 3 or 4, mai wins.

Explanation:

Step1: Calculate probability for each option

• Option A:

There are 3 names. Probability of each name being drawn is \(\frac{1}{3}\) since \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\) and total outcomes \(n = 3\), favorable outcomes for each \(m=1\).

• Option B:

When flipping a coin twice, total outcomes \(n(S)=2\times2 = 4\) (HH, HT, TH, TT). Probability of Anna winning (\(P(A)\)) (both heads - HH) is \(\frac{1}{4}\), probability of Jo winning (\(P(J)\)) (both tails - TT) is \(\frac{1}{4}\), probability of Mai winning (\(P(M)\)) (HT or TH) is \(\frac{2}{4}=\frac{1}{2}\).

• Option C:

When rolling a number - cube, total outcomes \(n = 6\). Probability of Anna winning (\(P(A)\)) (rolling a 1) is \(\frac{1}{6}\), probability of Jo winning (\(P(J)\)) (rolling a 2) is \(\frac{1}{6}\), probability of Mai winning (\(P(M)\)) (rolling 3, 4, 5, 6) is \(\frac{4}{6}=\frac{2}{3}\).

• Option D:

When rolling a number - cube, total outcomes \(n = 6\). Probability of Anna winning (\(P(A)\)) (rolling 1 or 6) is \(\frac{2}{6}=\frac{1}{3}\), probability of Jo winning (\(P(J)\)) (rolling 2 or 5) is \(\frac{2}{6}=\frac{1}{3}\), probability of Mai winning (\(P(M)\)) (rolling 3 or 4) is \(\frac{2}{6}=\frac{1}{3}\).

Answer:

A. Put each person's name on a separate piece of paper in a bag. Randomly draw the winning name.
D. Roll a number cube. If it lands on 1 or 6, Anna wins. If it lands on 2 or 5, Jo wins. If it lands on 3 or 4, Mai wins.