Multi-step Experiments

Student Summary

Suppose we have two bags. One contains 1 star block and 4 moon blocks. The other contains 3 star blocks and 1 moon block.

If we select 1 block at random from each, what is the probability that we will get 2 star blocks or 2 moon blocks?

Two bags of blocks. The bag on the left contains 5 blocks: 1 star block and 4 moon blocks. The bag on the right contains 4 blocks: 3 star blocks and 1 moon block.

To answer this question, we can draw a tree diagram to see all of the possible outcomes.

A tree diagram. The first choice has 5 branches, representing the 5 blocks in the bag: one branch is labeled “star,” the other 4 are labeled “moon.” Each of these branches has 4 branches, representing the 4 blocks in the second bag. 3 branches are labeled “star” and one is labeled “moon.” The word “star” in the first choice, and the 3 “star” choices branching from it are highlighted gold. From the first choice, the word “moon” is highlighted blue on each of the four remaining branches. From each of those branches, the one choice of “moon” for each is also highlighted blue.

There are 5⋅4=205 \boldcdot 4 = 20 possible outcomes. Of these, 3 of them are both stars, and 4 are both moons. So the probability of getting 2 star blocks or 2 moon blocks is 720\frac{7}{20}.

In general, if all outcomes in an experiment are equally likely, then the probability of an event is the fraction of outcomes in the sample space for which the event occurs.

Visual / Anchor Chart

Standards

Building On
5.OA.1

Apply the order of operations to evaluate numerical expressions.

6.EE.2.b

Write, read, and evaluate expressions in which letters stand for numbers.

Addressing
7.SP.8.a

Find probabilities of compound events using organized lists, sample space tables, tree diagrams, and simulation.

7.SP.8.b

Find probabilities of compound events using organized lists, sample space tables, tree diagrams, and simulation.