How Do You Compute Conditional Probability From Data?

It easy to confuse conditional probability with probability of an intersection of two event. They are related! The probability of an event A given that event B has occurred is

The vertical bar | means “given” and the event after it is the event that has already occurred.

Let’s look at some data to determine how to find several different probabilities including conditional probability.

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Technology Can Be Deceiving…

Suppose you are asked to determine whether a function is discontinuous. Many of you might use technology to help you graph a function to decide what the limits are from the left and right. Remember, a function is continuous at a point if the limits from the left and right are equal and also match the value of the function at the point.

Be aware that the TI calculators, WolframAlpha, and Desmos may give slightly different graphs and lead you to the wrong conclusion.

The new MathFAQ below demonstrates how to graph

in WolframAlpha and Desmos.

Notice how the graphs differ. Which one is the better graph to use if you are deciding if the function is discontinuous?

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How Do You Write Out The Solutions To A Dependent System of Linear Equations?

Dependent systems of equations are systems of equations that have many solutions. Typically when you solve a dependent system with substitution or elimination, you get 0 = 0. This indicates that many combinations of x and y will solve the system of equations…but how do you find those ordered pairs?

In the MathFAQ below, I demonstrate two strategies for writing out the solutions to dependent systems of linear equations.

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