Many factors need to be considered when buying a car, including style, color, gas mileage, and cost. Examine these choices and determine which represents a compound event.
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Based on the fundamental counting principle, the product of the number of options for color and the number of options for style must equal the total number of outcomes. If there are 8 total outcomes, the possible combinations of colors and styles are (1, 8), (2, 4), (4, 2), or (8, 1) because these are the pairs of factors that multiply to 8.
The Roberts family is shopping for a new vehicle. They are considering a minivan or an SUV. Each vehicle has three models; standard, sport, or luxury. The family has decided that they want a red vehicle. Explain how to make a tree diagram to show their options. How many choices do they have?
To create the tree diagram, start with two branches representing the styles of vehicle (minivan and SUV). From each of those two branches, draw three branches to representing the models (standard, sport, and luxury). Since the family has already decided on the color red, it does not need to be represented as a separate set of branches. In total, there are 6 possible choices (2 styles multiplied by 3 models).
What is Adele’s error?
The keyless entry system in some cars uses a 4-digit keypad. There are 10 possible digits, and the digits can be repeated. How many different combinations are there?1040✔ 10,00040,000
Adele also must choose between leather or cloth seats for her vehicle. Leather seats come in three color choices; brown, black, and blue. Cloth seats come in two color choices; tan and gray. Using multiplication, Adele says she has (2)(3)(2), or a total of 12, choices for seat covers. Is she correct? Explain why or why not.
Adele is incorrect. The fundamental counting principle is used for independent events where every choice in one category can be paired with every choice in another. However, here the colors are specific to the material type. There are 3 choices for leather and 2 choices for cloth, which means there are 3 + 2 = 5 total choices, not 12.
Many factors need to be considered when buying a car, including style, color, gas mileage, and cost. Examine these choices and determine which represents a compound event.
Question text not available
What is Adele’s error?
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