Evaluating FAIR OUTCOMES

Which of the following decision-making method is fair?

• Tossing a fair coin and using a random number generator

• Tossing a fair coin and spinning a slightly tilted roulette wheel

• Tossing a fair coin and dropping a fair die

• Tossing a fair coin and drawing from slips of paper of different sizes

Answer explanation

All other answers are clearly biased in one way or another. The slightly tilted roulette wheel would clearly land on the downward side more often,

dropping a fair die is still unfair because of the way it's tossed, and papers of different sizes introduce bias into the decision making process. Only a

random number generator would not.

Your friend wants to show you a magic trick and takes out a coin from her wallet. The coin is flipped several times in a row and all the results are heads.

What do you think?

• The coin is fair

• The coin is unfair

• This may have happened due to chance

• All answer options

Answer explanation

There is no mention of fairness in the question. Therefore, the coin may be unfair or fair. Theoretically, a coin can flip the same way an infinite number

of times and still be fair. It's statistically unlikely, but not impossible. She's either really good at manipulating the coin, it's unfair, or it's just a random

result.

You and your entire class are stranded on a desert island. A rescue boat can save all of you except for one, who will be left on the island forever. You

have all decided that whoever picks a number closest to the one that is randomly generated (luckily, someone brought a laptop) will stay behind. What

should be done to ensure a fair result?

• Make sure that everyone looks at each other while guessing

• Make sure that everyone writes their guesses down

• Allow

  people to talk to one another

• ALL answer choices

Answer explanation

Allowing people to talk to one another can make it more difficult and allow people to conspire against one particular person. Looking at each other can

either have no effect or can subtly convey messages to people via facial expressions, which could undermine the fairness. Writing down all the decisions

ensures no foul play after the number generator reaches its result.

The chances you will be struck by lightning are about 1 in 500,000 (depending on who keeps track). Would it be fair to say that if you and a group of

500,000 people were out in a field in the middle of a thunderstorm, only one of you would get struck?

• YES

• NO

• MAYBE

• NOT ENOUGH INFORMATION

Answer explanation

There are many factors at play here. Simply having a "herd" protection mentality isn't good enough based on statistics, since the numbers only describe

one chance event. For example, if you were standing in a soaking field with 500,000 people, lightning would only have to strike one point in the field to

electrocute everyone on it. (Remember, water conducts electricity.) This is an example of how to be careful interpreting statistics and how they were

gathered, what their data actually imply, and what assumptions these statistics make.

A marine sniper has a faulty weapon and needs to stay alive in a combat zone. He is able to hit a target that is 1 mile away 50% of the time, and a target

that is 100 feet away with only 10% accuracy (it really is a faulty weapon). Assuming 10 targets far away and 2 targets 100 feet away, which should he

target first in order to stay alive?

• Those closest to him, to avoid being shot

• Those farthest away because he has a much greater probability of hitting them

• Those farthest away because there are more of them

• None of the above

Answer explanation

Even though the probability of hitting those closest to him is lower, they are the greatest threat to his life right now. This is an example of when

probabilities should not overrule common sense.