Lesson: Challenging Problem Solving - 26t03

Basic Probability

When we use the term 'probably' in general conversation, we are usually referring to the chance, or the possibility, of a particular event or occurrence: "He'll probably win the match"; "She'll probably attend the meeting". Mathematical probability also involves possibilities and chance, but in far more precise manner. For our purposes, probability may be defined as follows: The example below will illustrate this concept:

In this scenario, we have a total of nine marbles—these marbles represent our possible outcomes. In selecting a marble randomly, we could choose any of the nine contained within the box.

Our desired outcome, however, is to select a blue marble. We don't care what blue marble we select—it just needs to be blue. We have 3 blue marbles we could choose, so we have 3 chances to obtain a blue marble.

Therefore, the probability of selecting a blue marble is:

Now use our sample question to determine the probability for each of the two selections that follow. For each one, enter your response into the textbox and then click Continue.

What is the probability that a green marble is chosen? _____

 

What is the probability that a red marble is chosen? _____

There are a total of nine marbles, four of which are red. Therefore, we have nine possible outcomes and four desired outcomes for a probability of .

Note that our combined probabilities equal 1:1, or 1: . If we were to select one marble at random from the box, the probability is that a blue, green, or red marble would be chosen—there are no other colors for any other outcome to occur. Therefore, the number 1 indicates 100% probability.

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