Module 5 – Introduction (Probability)
a) • If you try a “walkthrough” or video and it doesn’t work, you might try a different browser to see if it works.
• You should do all of the walkthroughs, “learn by doing”, and “did I get this” in the Module!
b) a good point:
“Recall from the Sampling module that when we say that a random sample represents the population well we mean that there is no inherent bias in this sampling technique. It is important to acknowledge, though, that this does not mean that all random samples are necessarily “perfect.” Random samples are still random, and therefore no random sample will be exactly the same as another. One random sample may give a fairly accurate representation of the population, while another random sample might be “off,” purely due to chance. Unfortunately, when looking at a particular sample (which is what happens in practice), we will never know how much it differs from the population. This uncertainty is where probability comes into the picture. We use probability to quantify how much we expect random samples to vary.”
c) It is noted in the text that the prior 2 examples were Hard, Complex.
We conclude that probability is not always intuitive.
I want to clarify this point:
Some Probability is clear; we get it intuitively.
The rest takes experience and practice to get it.
(It might seem hard, but is actually just unfamiliar and sometimes complex.)
d) Notation and facts: P(A) means “the probability that an event A will occur”
The probability that an event will occur is between 0 and 1.
That is: 0 ≤ P(A) ≤ 1.
Exer. 1: What is P(someone will be absent from class the next class period)?
Exer. 2: What is P(it will rain sometime between November and April in Tacoma) ?
Exer. 3: What is P(next time I come into class I will be six feet tall – I am now 5’3”)?
Answers: 1) not sure but fairly high, maybe 80% 2) 1 3) 0
A probability can be expressed as a percent, or as an equivalent fraction, or as an equivalent decimal.
Example: P(a fair coin lands heads when it is tossed) = 50% = 1/2 = 0.5
e) Two approaches to probability
• Theoretical (also known as Classical)
Example: the theoretical (or classical) approach to probability was used to state P(Heads) = ½.
• Empirical (also known as Relative Frequency or Observational)
f) Relative frequency can be used to estimate a probability of an event.
This is an empirical or observational approach.
Simulations are useful for exploring relative frequency estimates of probability.
The probability of event A is the relative frequency with which the event occurs in a long series of trials.
Example: The empirical approach can be used to find this:
In a certain population, what is the probability that a randomly selected person has blue eyes?