Probability- Math Week 6 Critical Thinking

Math Week 6 Critical Thinking Name MTH109-1 – Mathematical Explorations Colorado State University – Global Campus Instructor Date Introduction Probability is necessary to analyze random phenomena and for random experiments, there are a set of values that are determined by chance or the likelihood they may or may not occur. In probability, the sample spaces are used when there is a set possible outcome of a randomized experiment (CSU, 2016). An event is any subset of sample points and the theory of probability focuses on quantifying the chance of occurrence of an event chance and uncertainty. In situations where there are several possible outcomes, probability is necessary when there is focus on chance and uncertainty. When there is a large number of sample points, identifying the sample points and the associated probabilities is cumbersome and at times impossible (Anderson et al., 2017). Probability calculations are required for the analysis methods of the behavior of random phenomena such as rolling a die, choosing diamond from a deck of cards and the expected outcomes. Rolling a dice The odds in favor of a five being rolled on a single die and probability are determined. There are six sides of the dice and rolling a 5 is determined as probability of rolling a five divided by the probability of not rolling a fives. Thus p: q=1/6 ÷ 5/6= 1:5. The probability (p) of rolling a 5 is 1/ 6 or 16.7%, which is the number of fives÷ total possible outcomes while the probability (q) of not rolling a 5 is 5/6. In the case of throwing a dice, the more times the experiment is repeated, the more likely that the relative frequency, that is, the probability of occurrence of obtaining a 1, 2, 3, 4, 5 or 6 is 16.7%. Throwing of a dice is a random experiment, since the experiment can be repeated under the same conditions and all the possible outcomes are known despite not being sure of the final outcomes. All possible results of a randomized experiment as represented by the sample space is E = {1, 2, 3, 4, 5, 6}. Classical probability represents the ratio between the number of favorable cases (events), and the total number of possible cases events where the events are mutually exclusive and equally possible. There is an assumption that events are equiprobable such that they have equal probability of occurring. An experiment in probability is any process or action that generates observations and that can be repeated including throwing a dice. Randomized experiments such as throwing a dice are based on chance, where they can be repeated indefinitely and always under the same conditions. Any subset of the sample is an event and the probability of occurrence of a given event, is the ratio between the number of times that event occurred and the number of repetitions of the experiment and this is also the relative frequency.Probability of holding a diamond card The concept of probability when analyzing the cases focuses on information about the sample space and the likelihood of dealing one or more card from the deck of 52 cards and each card represents a sample point with a 1/52 prob...