PSYC 3002 – Week 3 Discussion – Probability in Real Life

PSYC 3002 – Week 3 Discussion – Probability in Real Life

“The experiment of tossing a fair die” was the example I chose for this discussion.

If we toss a fair die, what is the probability of each sample point? For this experiment, the sample space consists of six sample points: {1, 2, 3, 4, 5, 6}. Each sample point has equal Probability. And the sum of probabilities of all the sample points must equal 1. Therefore, the Probability of each sample point must be equal to 1/6. https://stattrek.com/probability/probability-problems.aspx

In statistics, Probability helps us understand that the likelihood of the results of an experiment is not due to chance (Laureate Education, Producer, 2015k). According to Heiman (2015), Probability is used to describe events that occur randomly or by chance. In other words, one event has no bias over another; it all occurs by chance. These events that occur randomly or by chance are referred to as samples, and the collection of all these possible random events in an experiment is called the population. From our above example of tossing a fair die, a sample could be; 1, 2, 3, 4, 5 or 6. Then the population is the collection of all possible sample points; 1, 2, 3, 4, 5 and 6.

From our experiment, when we toss a fair die in order to ascertain that an event occurs by chance or randomly, we observe how often the event occurs over the long run. If event that the sample point 1 occurs more frequently as we toss the die, we can conclude that the sample point 1 has a high probability. Likewise, if the event that sample point 5 does not occur frequently over the long run, we say that it has a low probability. Therefore the term “over the long run” refers to how frequently an event will occur in the population of possible events.

PSYC 3002 – Week 3 Discussion – Probability in Real Life

If, for instance, we toss the fair die a couple of times and observe that one event, say sample point 6, occurs more frequently in the population, then we are describing the event’s relative frequency. The relative frequency, which is equal to an event’s Probability, is defined as the proportion of time that an event occurs out of all events that might occur in the population (Heiman, 2015).

The “gambler’s fallacy” is a term Psychologists use to describe people who fall victim to the fact that Probability implies over the long (Heiman, 2015). In our tends to occur more frequently, the fallacy would be thinking that sample point 6 is now less likely to occur, essentially concluding that other sample points have become more likely. This is because sample point 6 has already occurred too often. But what the gambler’s fallacy fails to recognize is that the Probability of an event occurring is not affected by whether or not the event occurs over the short run: Probability is determined by what happens over the long run.

This example above strengthened my understanding of statistical Probability, relative frequency to be precise, with reference to this; A bulb manufacturing company decided to ascertain if the company was manufacturing good or defective bulbs by selecting a random sample of one hundred fifty bulbs from a certain big lot for the examination. After the examination was conducted, it was discovered that 80 bulbs out of 150 were defective. By computing the relative frequency;

Let N be the number of bulbs randomly selected = 150. Let f be the frequency = 80

Relative frequency = f/ N = 80/150 = 0.53

We can conclude that the proportion of defective bulbs produced by the company is 0.53

References

Heiman, G (2015) Behavioural Sciences STAT (2nd ed.). Stamford, CT: Cengage.

Laureate Education (Producer). (2015k). Probability and introduction to inferential statistics [Video file]. Baltimore, MD: Author.

The experiment of tossing a fair die.https://stattrek.com/probability/probability-problems.aspx

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