Rolling dice can have different results with every roll. The same is true with drawing cards in a card game or from the deck. Furthermore, the same concept may occur when predicting probability of winning a game. Therefore, probability, known as the likelihood of an occurrence, is a tremendous part of rolling dice (Spiegel, Schiller, Srinivasan, & LeVan, 2009). Therefore, probability is commonly used to determine the likely results of a single roll or a set of rolls, which results in a sample space (range of values of random rolls). These values are from the event (defined as the outcomes which probability is assigned to) (Spiegel, Schiller, Srinivasan, & LeVan, 2009). The purpose of this report is to explore probability in conjunction with rolling dice.
Methodology and Discussion
The first set of information states: “Two four-sided dice are rolled. One die has the numbers 1, 2, 3, and 4. The other has the numbers 5, 6, 7, and 8.” The first portion of the inquiry is to determine the number of elements in the sample space. This is calculated by adding the number of possible outcomes. The possible outcomes are [1, 5], [1, 6], [1, 7], [1, 8], [2, 5], [2, 6], [2, 7], [2, 8], [3, 5], [3, 6], [3, 7], [3, 8], [4, 5], [4, 6], [4, 7], and [4, 8]. Therefore, there are 16 elements in the sample space. For some statisticians, this is expressed as P (x) + P (y) … + P (z). At the same time, it is possible to express the event that both die sum to be 8 as a set. This is by stating that P (8) = [1, 7], [2, 6], and [3, 5]. Therefore, the probability that the total is equal to 8 can be found by noting the number of combinations that equal 8 (which is 3) and the possible outcomes, which is 16. Thus, the probability that the total is equal to 8 is 3 to 16, otherwise expressed as: 3 / 16 = 0.1875. When selecting three Jacks from a 52-deck of cards, the probability of selecting three Jacks is calculated as: (4 / 52) * (3 / 51) * (2 / 50) = 14 / 132600 = 2 / 66300 = 0.00018099. When determining the odds in favor of Tem B winning, the formula used is: 1 – (Probability of Team A Winning) = 1 – (7 / 12) = 5 / 12 = 0.41667.
Probability is used in a variety of situations. Rolling dice and playing cards are prime examples of ways that probability is used. When rolling dice, it is possible to determine the probability of obtaining a particular combination or specific number. For a single die, this would be shown as x / y, where x is 1 and y is the total options, such as (1 / 6). For a particular roll, this would be shown as x / y, where x is the possible occurrences and y is the total options. This report, for instance, showed that the probability of rolling a combination that results in a sum of 8 with two dice, one as 1, 2, 3, 4 and the other with 5, 6, 7, 8 is 3 / 16 or 0.1875. Thus, the likelihood of this combination is 18.75%. This same concept can be used in other instances, as well. When drawing cards, it is important to consider whether or not the card is returned to the deck or kept. This means that the available possibilities will decrease if the card is kept.
- Spiegel, M. R., Schiller, J. J., Srinivasan, R. A., & LeVan, M. (2009). Probability and statistics (Vol. 2). New York, USA: McGraw-Hill.