Question

question 23 of 25
angel and isaiah have forgotten whose turn it is to mow the lawn. how can
they make a fair decision?
select all the correct answers.
a. flip a coin. if it comes up heads, angel mows the lawn. if it
comes up tails, isaiah mows the lawn.
b. flip a coin twice. if either toss is tails, angel mows the lawn.
otherwise, isaiah mows the lawn.
c. put each persons name on a separate piece of paper in a bag.
randomly draw a name. the person whose name is chosen
mows the lawn.
d. roll a number cube. if the number rolled is 1 or 6, angel mows the
lawn. if it is any other number, isaiah mows the lawn.

Explanation:

Step1: Analyze option A

A fair coin has two equally - likely outcomes (heads and tails). The probability of heads \(P(H)=\frac{1}{2}\) and the probability of tails \(P(T)=\frac{1}{2}\). So, each person has an equal chance (\(50\%\)) of being selected.

Step2: Analyze option B

When flipping a coin twice, the sample space is \(S = \{HH, HT, TH, TT\}\). The probability that either toss is tails \(P(\text{at least one tail})=\frac{3}{4}\) and the probability that both are heads \(P(HH)=\frac{1}{4}\). So, the probabilities for Angel (\(\frac{3}{4}\)) and Isaiah (\(\frac{1}{4}\)) are not equal.

Step3: Analyze option C

There are two names in the bag. The probability of drawing Angel's name \(P(\text{Angel})=\frac{1}{2}\) and the probability of drawing Isaiah's name \(P(\text{Isaiah})=\frac{1}{2}\). Each person has an equal chance of being selected.

Step4: Analyze option D

A standard number cube has 6 faces. The probability that the number rolled is 1 or 6 \(P(1\text{ or }6)=\frac{2}{6}=\frac{1}{3}\), and the probability that it is another number \(P(\text{other})=\frac{4}{6}=\frac{2}{3}\). So, the probabilities for Angel (\(\frac{1}{3}\)) and Isaiah (\(\frac{2}{3}\)) are not equal.

Answer:

A. Flip a coin. If it comes up heads, Angel mows the lawn. If it comes up tails, Isaiah mows the lawn.
C. Put each person's name on a separate piece of paper in a bag. Randomly draw a name. The person whose name is chosen mows the lawn.