MHB What is probability and how does it relate to precalculus?

[mathdad]

Most students struggle with probability because questions usually involve FUZZY word problems. I am reviewing precalculus right now. In the later chapters of precalculus, a touch of probability is introduced.

Can someone explain the basics of probability? I know, for example, that all probabilities fall between 0 and 1, which means all probabilities are fractions. What is probability? I need a simple definition with maybe one or two basic problems.

 

[MarkFL]

A probability is a measure of the likelihood of some event taking place. It is the ratio of the number of favorable outcomes divided by the number of total outcomes. A probability of 0 means the event is impossible, while a probability of 1 mean the event is certain.

For example, suppose we wish to compute the probability that when rolling a six-sided die, we will get an even number. Since there are 3 faces with even numbers, and 6 total faces, we would give the probability as 3/6 = 1/2. If we label the event X then it is standard to denote this as:

P(X) = 1/2

Suppose we call event Y getting an odd number...now we could easily compute this directly, but I want to highlight a useful technique in the study of probability for computing otherwise difficult probabilities. We could reason that it is certain we will either get an even number or an odd number...mathematically this is:

P(X) + P(Y) = 1

Hence:

P(Y) = 1 - P(X) = 1 - 1/2 = 1/2

There is much more to probability, but it would be better to deal with those questions as they arise. :D

 

[mathdad]

Of course, I will continue with precalculus questions and post probability in this forum from time to time.