Glossary: Coin Toss

Coin Toss Example

Consider, for example, the number of possible 3-coin outcomes when three coins are tossed simultaneously. Note first of all that there are only two outcomes possible for each coin, heads or tails, each with a probability of 1/2, or.50 (on a fair coin). Now note the various probabilities for the 3-coin outcomes below:

H H H  = 1/8

H T H  = 1/8

H H T  = 1/8

T H H  = 1/8

T H T  = 1/8

H T T  = 1/8

T T H  = 1/8

T T T  = 1/8

 

 

Note that, when selection is truly random, the possibility of obtaining a single outcome three times in a row (i.e., 3 heads or 3 tails) is small (1/8 + 1/8 = 2/8 or 1/4). In contrast, the probability of obtaining a heads/tails combination is much greater (6/8 or 3/4). Thus, although there is always a small chance that we will end up selecting cases from only one group in the population (similar to getting all heads or all tails), it is much more unlikely than selecting cases from several groups in the population (i.e., heads/tails combinations).

Furthermore, the chances of obtaining only members from one subgroup in the population will further decrease as the number of cases selected increases (this would be equivalent to flipping 4 coins instead of 3; note that for 4 coins, the probability of getting all heads or getting all tails has now fallen to 2/16 or 1/8).

Thus, while random selection and proper sampling procedures are not full proof, they are still the best options to use when choosing a working sample that is meant to be representative of the overall population from which the sample is drawn.