Identify the number of occurrences for each possible outcome.
See solution.
Practice makes perfect
We want to use the scenarios given in Explorations 3 and 4 to make some general observations. Let's look at each Exploration one at a time.
Exploration 3
Let's look at the spinner from Exploration 3.
We can see that the spinner has 12 sections. Therefore, there are 12 total outcomes. Looking at the different sections, we can see that the possible outcomes are the integers from 1 to 5. Let's list these outcomes in a table with the number of occurrences for each one. We can also write the ratio of the number of occurrences to the total number of outcomes.
We have 7 choices to pick from when choosing the first ball and 6 choices to pick from when choosing the second ball. By the Fundamental Counting Principle, we can find the total number of outcomes by multiplying these numbers.
7* 6 = 42
From the given information, we know that the possible outcomes of the experiment are picking two blue, blue then red, red then blue and two red.
B B, B R, R B, R R
Once again, let's make a table to display the possible outcomes, the number of occurrences, and the ratio of the number of occurrences to the total number of outcomes. To find each occurrence, we need to multiply the number of balls of the first color by the number of remaining balls of the second color.
We can see that adding the occurrences of every outcome adds up to the total number of outcomes. This is because the sample spaces are complete, and every possible outcome is considered. Because the addition of the occurrences add up to the total number of occurrences, the sum of the ratios adds up to 1.
