7th Grade Compound Events and Simulations Lesson (Free PDF)
This compound events lesson for 7th Grade covers compound events and simulations (Common Core 7.SP.C.8), with a free PDF to print.
A compound event combines two or more simple events. Its probability is found by counting the favorable outcomes in the sample space, which you can list in an organized list, a table, or a tree diagram. A simulation uses random numbers to estimate the probability when counting is difficult.
Grade 7 · Common Core State Standards: 7.SP.C.8
Key facts in this compound events lesson
- A compound event has two or more stages, such as two coin tosses.
- The sample space lists every possible outcome.
- Counting principle: \(m \times n\) outcomes for two stages with m and n ways.
- Equally likely outcomes: \(P = favorable \div total\).
- A simulation uses random numbers to estimate a probability.
What is a compound event?
A compound event consists of two or more simple events, such as tossing a coin and rolling a die, or rolling two dice. The sample space is the set of all possible outcomes.
How do you list the sample space?
Use an organized list, a table, or a tree diagram so that no outcome is missed.
For two tosses, the outcomes are HH, HT, TH, and TT. They are equally likely, so \(P(\text{two heads}) = \frac{1}{4}\), and \(P(\text{at least one head}) = \frac{3}{4}\) because three outcomes contain a head.
How do you use a table for two dice?
Two dice have \(6 \times 6 = 36\) outcomes. A table of sums shows how many ways each sum can occur.
What is a simulation?
A simulation imitates a chance event with random numbers, a spinner, or coins. If a shooter makes 60% of free throws, let the digits 0 to 5 mean “made” and 6 to 9 mean “missed.” Each pair of digits is one trial of two shots. The fraction of trials with two made shots estimates the probability.
With replacement means the first item goes back before the second is chosen, so the probabilities do not change. Without replacement, the second probability depends on the first draw. Always say which one is used.
Compound events lesson: questions and answers
What is a sample space?
It is the set of all possible outcomes of an experiment. For two coin tosses it is HH, HT, TH, and TT.
How do you use a tree diagram?
Draw a branch for each outcome of the first event, then branches from each for the second event. Each path from left to right is one outcome.
How many outcomes do two dice have?
Each die has 6 outcomes, so there are \(6 \times 6 = 36\) outcomes.
What is the difference between with and without replacement?
With replacement the first item goes back, so the second draw has the same chances. Without replacement the chances change.
How does a simulation estimate probability?
Assign random digits to outcomes, run many trials, and divide the number of successful trials by the total. More trials give a better estimate.
How to use this compound events lesson
Read the definitions first, then follow the worked method line by line and redo the example on paper without looking. When every step makes sense, move on to the worksheet, then check yourself with the quiz.
Download the compound events lesson as a PDF with the button below and keep it with your notes.
All Grade 7 chapters: Grade 7 math.
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