Statistics

Game of Roulette

In statistics, probability and odds are two different concepts. The difference between the two can be derived from the way the two are calculated.

_{probability =}  Number of desirable outcomes

                  Number of possible outcomes

_{odds =}  Number of desirable outcomes

             Number of undesirable outcomes

In roulette bets, if the ball lands on a number that is not among those selected, then the player loses the bet. There are various roulette bets. Assuming that the wheal is fairly balanced, the average probability of the ball falling on any number is 1/38 (Peter, 2001). This implies that, on average, every 38 wheel spins will lead to 37 loses and a single win.

For a bet on a single number: 0, 00, or 1-36. If a player wins, the payoff is 35: 1 implying that he gets his original chip back plus 35 more chips. In other words, he starts with 1 chip and wind up with 36 chips. Depending on the bet and where the ball stops, there are various payoffs. The 0 and 00 Slots are colored green and all the others are colored red or black, half of each color.

As mentioned earlier, a win following a bet on a single number leads to a payoff of 35: 1. This implies that the player gets 35 extra chips, in addition to his original chip.  The probability of the ball landing on the correct number (1-16 or 0) following a spin is assumed to be 1/38. The implication is that the ball will land on each number one time in every 38 spins. For the 38 spins, the average loss is 37. Betting on half of the non-green numbers pays 1: 1. This implies that the player doubles his money on every win.

Nevertheless, all modes of betting have the same advantages in the long run. When a player bets on a single number as in the former case, he loses 37 chips as he gains 35 on average. This means that the player’s expected value is -2/38. Therefore, the American roulette has an expected return of -1/19 per bet. The reasoning here is that a player loses 1/19 of the money that he bets. In the latter case, a player tries his luck on a half of all non-green numbers. The expected average win in this case for every 38 bets is 18, and; therefore, the expected loses is 38-18=20. Since the payoff in such a scenario is 1:1, a player receives 1 chip for every win, and this gives a total of 18×1=18 wins. Consequently, the average net loss in 38 turns will be 20-18=2. This implies that a player loses 2/38=1/9 of his money. The loss is equal to that of the previous case, and this means that the returns on all modes of betting are the same.

Objectives

Collecting accurate data in research enhance the validity of the results. To ascertain the accuracy of the data, it is vital for a researcher to choose the right kind of method, while taking into account the characteristics of the data being targeted. There are two categories of data collection methods: qualitative and quantitative methods. With quantitative methods, structured collection instruments are used to collect data on random samples that are assumed to represent the real world. These instruments help in fitting varying data into preset response categories that facilitate summarization, comparison, and generalization. Qualitative methods are used in collecting data for use in testing hypotheses and estimating the size of phenomena (Christian, 2010). There are several quantitative data collection strategies. They include experimentation, observation with recording, and surveys. On the other hand, qualitative methods are used during the evaluation of impacts. They provide useful information that helps in understanding the procedures behind the observable results. They also help in assessing people’s changes in perception regarding their welfare. They, therefore, enhance the quality of quantitative evaluation as they assist in generating evaluation hypotheses as well as expanding the quantitative findings. These methods are classified into in-depth interviewing, observation, and document review.

Risk assessment involves determining the qualitative or quantitative risk value that relates to a specific situation with regard to an identified threat. In quantitative assessment, calculations of due risk components are undertaken i.e., the size of the expected loss L, and its probability p of occurrence. The methods used in assessing risk depend on the industry involved and the kid of assessment needed. Assessment may be environmental, financial, ecological, or employee satisfaction.

A business can use various statistical tools to monitor its activities. These tools include t-test and f-test. The management can use t-test while testing hypotheses regarding the mean when a sample is small. T-distributions are symmetric, and they resemble normal distributions. They actually tend to be normal with the increase in sample size. In t-tests, the variances of the two samples are assumed to be equal. On the other hand, f-tests are used in testing hypotheses regarding variances. F-distributions are based on ratios of chi squires. These distributions are usually asymmetrical (Christian, 2010). These statistical tools help in business development, technical sales, and product marketing.

Effective communication marks the difference between failure and success of businessperson. These techniques help individuals to overcome competition as they can convince and win the confidence of the majority of stakeholders. For effective communication, one need to have clear objectives, understand his/her audience, match his method to the message being conveyed, be attentive with details, obtain feedback, and stay focused.

Problem solving includes finding a problem and shaping it. It is an intellectual function that is complex and requires modulation of more fundamental skills. The process of finding a solution occurs when a team wishes to accomplish a desired goal (Christian, 2010). When a problem or project is being tackled by a team, the shaping and result formulation becomes easier. Working as a team helps improve communication. It also motivates the individual members to learn vital self-regulation strategies thereby improving their productivity.