standard_description: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).
problem_activity: Problem 1
Each scenario on the left corresponds with a calculation on the right. Connect the scenarios and calculations and identify which features are most useful in connecting the representations:
{"table": [{"_attributes": {"align": "center", "class": ["table", "table-bordered"], "style": "table-layout:fixed; width:60%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Rolling once the number is an odd number or a number less than 3."}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${P(A\\space\\mathrm{and}\\space B) = \\left({3\\over6}\\right)\\left({1\\over6}\\right)}$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Rolling once and the number is an odd number or 4."}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${P(A\\space\\mathrm{or}\\space B) = {3\\over6}+{2\\over6}-{1\\over6}}$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Rolling twice. The first roll is an odd number and the second roll is a number less than 3."}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${P(A\\space\\mathrm{and}\\space B) = \\left({3\\over6}\\right)\\left({2\\over6}\\right)}$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Rolling twice. The first roll is an odd number and the second roll is a 4."}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${P(A\\space\\mathrm{or}\\space B) = {3\\over6}+{1\\over6}}$$"}]}]}]}]}]}
Problem 2
Below is a spinner with four quadrants, each labeled 1–4. Each outcome is equally likely.
[IMG]
Sam spins the spinner twice and doesn’t land on 4. What is the probability of this occurring?
Problem 3
Allison has put together a simple game. She put 6 cubes in a paper bag—3 yellow and 3 blue. Allison has determined that the rules are as follows:
Pull a cube from the bag and put it on the table.
Pull a second cube from the bag.
If the cubes are different colors, then Player A wins.
If the cubes are the same color, then Player B wins.
Is this game fair? How do you know?


aligns: yes