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Clarifications: Each clarification provides an explanation of the indicator/objective to help teachers better understand the concept. Classroom examples are often included to further illustrate the concept. While classroom examples could be shared with the students, the intended audience for the explanation/clarification is the classroom teacher-not the student. In addition, classroom examples may or may not reflect the assessment limits.

Standard 5.0 Knowledge of Probability

Topic B. Theoretical Probability

Indicator 2. Determine the probability of a second event that is dependent on a first event of equally likely outcomes

Objective a. Express the probability as a fraction, a decimal, or a percent

Assessment limit: Use a sample space of no more than 60 outcomes

Clarification

Use a tree diagram along with probabilities for the events at each stage of the experiment to compute the theoretical probability of dependent events. Suppose you have two red chips and one blue chip in a bag. You will draw one chip out of the bag and then, without replacing the first chip, draw another chip from the bag. This is the tree diagram for that compound event made up of dependent events. The probabilities of each separate event are shown along the branches.

tree diagram

The sample space for this event is {RR, RB, BR}. Notice that when selecting a blue chip first, the only chips left in the bag are red. That is why the probability of drawing a red chip after drawing a blue chip is 1.

Classroom Example 1

Mary, Jerry, Terry, Barry and Larry volunteer to work in the school's main office. The principal needs only 2 students. First the principal selects Jerry. What is the probability that he will then select Larry?

Answer:

Since Jerry is no longer in the pool of students to be selected, there are only four students: Mary, Terry, Barry and Larry. The probability of selecting Larry from this group is 1/4.

Classroom Example 2

There are 4 blue chips, 2 red chips and 1 yellow chip in a bag. If a red chip is draw from the bag and not replaced, what is the probability of then drawing another red chip?

Answer:

There are 7 chips in the bag. If a red chip is drawn from the bag and not replaced there are 6 chips in the bag and 1 of them is red. The probability of drawing the second red chip is 1 out of 6 or 1/6.
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Resources for Objective 5.B.2.a:
CLARIFICATIONS | Sample Assessments |