Reba tosses a coin 20 times. She obtains 14 heads and 6 tails. Reba concludes that this coin is not a fair coin. Which of the following is true?
A) Reba is probably right, because if the coin were fair, she would have obtained exactly 10 heads and 10 tails.
B) Reba is probably right if the outcome of heads cluster together instead of being spread out.
C) Reba is probably wrong, because theoretical probability never happens in real life.
D) Reba is probably wrong, because empirical probability approaches theoretical probability only with an infinitely large number of tosses.

Question

Quizplus · Accepted Answer

Reba's conclusion is based on empirical probability, which is the result of actual trials. However, empirical probability tends to approach theoretical probability, which is the expected outcome based on probability calculations, only with an infinitely large number of trials. Therefore, it is possible for Reba to obtain 14 heads and 6 tails even with a fair coin. Choice A is incorrect because obtaining exactly 10 heads and 10 tails is only the expected outcome for a fair coin, but it is not a guarantee. Choice B is incorrect because the clustering of outcomes is not a reliable indicator of a fair or biased coin. Choice C is incorrect because theoretical probability does happen in real life, but it is not a guarantee for any specific set of trials.

Reba Tosses a Coin 20 Times