Question

An ancient Roman coin is found and a curious anthropologist wishes to determine if the coin is fair— Fair meaning that when flipped, it has a 50% chance of landing one way or the other. The anthropologist flips the coin 100 times and the coin comes up heads 72 times. Do you believe the coin is fair? What range of results would you expect if the coin was indeed fair?

Answer 1

The coin wouldn't be fair, because it landed on heads 72/100 times. If the coin was fair, the results should be equivalent to 1/2.

Answer 2

The coin is not fair.

Explanation:

We have been given that an ancient Roman coin was flipped 100 times by an anthropologist and the coin comes up heads 72 times.

Since we know that a fair coin has an equal chance of coming up heads or tails. This means probability of getting heads on one flip is 1/2 or 50%. Let us find probability of heads in anthropologist's experiment.

`Probability=\frac{\text{The number of favorable outcomes}}{\text{Total  umber of possible outcomes}}`

`P\text{H}=(72)/(100)`

`P\text{H}=0.72`

Since the probability of getting heads in anthropologist's experiment is 0.72 or 72%, therefore, the coin is not fair. If the coin was indeed fair we would expect approximately getting 50 heads in 100 flips.