You may feel it's obvious that the probability of a head in...

You may feel it's obvious that the probability of a head in tossing a coin is about $1 / 2$ because the coin has two faces. Such opinions are not always correct. Stand a nickel on edge on a hand, flat surface. Pound the surface with your hand so that the nickel fulls toner. Do this 25 times, and second the results. (a) What's your estimate for the probability that the coin falls heads up? Why? (b) Explain how you could get an even better estimate.

You may feel it's obvious that the probability of a head in tossing a coin is about $1 / 2$ because the coin has two faces. Such opinions are not always correct. Stand a nickel on edge on a hand, flat surface. Pound the surface with your hand so that the nickel fulls toner. Do this 25 times, and second the results.
(a) What's your estimate for the probability that the coin falls heads up? Why?
(b) Explain how you could get an even better estimate.

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Key Concepts

Experimental Probability

Experimental probability is an estimate of the likelihood of an event determined by performing an experiment and calculating the ratio of the number of times the event occurs to the total number of trials. It is particularly useful when the theoretical probability is hard to compute or when physical factors might alter the ideal assumptions of equal likelihood.

Relative Frequency

Relative frequency refers to the ratio of the number of times a specific outcome occurs to the total number of trials in an experiment. It serves as an approximation of the true probability of an event, especially when outcomes are derived from repeated experiments.

Sample Size

Sample size is the number of trials or observations used to compute an estimate in an experiment. A larger sample size generally provides a more reliable estimate of the true probability, reducing the variation or error that comes from a small number of observations.

Law of Large Numbers

The law of large numbers is a principle that states as the number of trials in an experiment increases, the experimental probability (or relative frequency) of an event tends to approach its true theoretical probability. This concept underlines why increasing the sample size can lead to a more accurate estimation of probabilities.

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