Probability gives us a way to numerically quantify the likelihood of something occurring. Some probabilities are second

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Probability gives us a way to numerically quantify thelikelihood of something occurring. Some probabilities are secondnature to us as we have seen them through the course of our lives.For example, we might know that the chances of heads landing faceup when I toss a coin are 50%. Probability is one of the mistfundamental tools used in statistics and we will see it arise as wecontinue through the class.
Probabilities are reported as values between 0 and 1, but weoften report them as percentages as percentages make more sense tothe general population. A probability of zero means somethingcannot happen. A probability of 1 means something is guaranteed tohappen. The closer my probability is to 1, the more likely theevent is to occur. The close my probability is to zero, the lesslikely the event is to occur.
There are three main types of probabilities we see:
Classical Probability – Classical probability is also known asthe “true” probability. We can compute classical probability aslong as we have a well-defined sample space, and a well-definedevent space. We compute the probability of an event E asfollows: P(E)=n(E)n(S) when n(E) refers to thenumber of elements in our event space and n(S) refers tothe number of elements in our sample space. For example, let’s takea look at a six-sided die. We can define our sample space as alloutcomes of the roll of the die, which gives us the following: S ={1,2,3,4,5,6}. If we let our event E be that the outcome is thenumber 3, our event space becomes the following: E = {3}. In orderto compute the classical probability, we take the number ofelements in our event space and divide it by the number of elementsin our sample space. This example gives us P(E)=n(E)n(S)=1/6.So, the probability of rolling the number 3 will be 1/6.
Empirical Probability – Empirical probability, also known asstatistical probability or relative frequency probability, isprobability calculated from a set of data. We compute it the exactsame way we computed relative frequency by taking the number oftimes our event occurred divided by the number of trials we ran.The formula is asfollows: P(E)=FrequencyofEventETotalFrequency. Taking a lookat the die example, we can run an experiment where we roll a die 20times and count the number of times the value 3 shows up. Supposewe do this and see that in 20 rolls of a six-sided die, the number3 shows up five times. We can compute the empirical probability asfollows: P(E)=FrequencyofEventETotalFrequency=5/20=1/4.. Wenow see that based on our experiment, the probability of rolling a3 was found to be ¼.
The law of large numbers tells us this: As my sample sizeincreases, the empirical probability of an event will approach theclassical probability of the event. When we have smaller samplesizes, we can often see oddities arise. For example, it is entirelypossible to flip a fair coin and see the value of heads arise 5times in a row, or even 9 times out of 10. Our empiricalprobability is far off our classical probability at this point intime. However, if I continue to flip my coin, I will see myempirical probability starts to approach our classical probabilityvalue of 0.5.
Subjective Probability – Subjective probability comes fromeducated guess, based on past experiences with a topic. Forexample, a teacher might say that if a student completes all theirStatistics assignments before the due date, the probability theypass the course is 0.95.
Instructions
For this discussion, we are going to run an experiment flippinga coin. Follow these steps and record your results:
Step 1 – Flip a coin 10 times. Record the number of times Headsshowed up.
Step 2 – Flip a coin 20 times. Record the number of times Headsshowed up.
Discussion Prompts
Respond to the following prompts in your initial post: