Ohio Resource Center
Assessments
NAEP Assessment Item, Grade 12: Find the Probability When Tossing a Coin
Discipline
Mathematics
7, 8, 9, 10, 11, 12
Professional Commentary

Students are asked to determine the probability that 2 heads and 1 tail will come up, in any order, if a fair coin is tossed three times. Students have the option to use a calculator. This constructed-response question is a sample test item used in grade 12 in the 1990 National Assessment of Educational Progress (see About NAEP). The URL link (above) takes the user directly to the NAEP test item, with access to performance data by various subgroups of students, a scoring guide, sample student responses, and a discussion of the content on which the item is based. The NAEP website allows users to build their own printable database of test items by clicking on Add Question in the upper right hand corner of the screen. NAEP Reference Number: 1990-12M9, No. 17. (sw)

Ohio Mathematics Academic Content Standards (2001)
Data Analysis and Probability Standard
Benchmarks (5–7)
H.
Find all possible outcomes of simple experiments or problem situations, using methods such as lists, arrays and tree diagrams.
I.
Describe the probability of an event using ratios, including fractional notation.
Benchmarks (8–10)
H.
Use counting techniques, such as permutations and combinations, to determine the total number of options and possible outcomes.
J.
Compute probabilities of compound events, independent events, and simple dependent events.
7.
Compute probabilities of compound events; e.g., multiple coin tosses or multiple rolls of number cubes, using such methods as organized lists, tree diagrams and area models.
10.
Calculate the number of possible outcomes for a situation, recognizing and accounting for when items may occur more than once or when order is important.
11.
Demonstrate an understanding that the probability of either of two disjoint events occurring can be found by adding the probabilities for each and that the probability of one independent event following another can be found by multiplying the probabilities.