Laundry Symbols Based on a New Generation of Stains survey, 13% o...

4. Probability

Complements

Statistics

4. Probability

Complements

1:18 minutes

Problem 4.2.7

Textbook Question

Laundry Symbols Based on a New Generation of Stains survey, 13% of U.S. adults know that the care-instruction symbol on clothing means that any bleach can be used. Find the probability of randomly selecting an adult in the U.S. who does not know that.

Verified step by step guidance

Step 1: Understand the problem. The problem states that 13% of U.S. adults know the care-instruction symbol for any bleach. This means the probability of knowing is 0.13. We are tasked with finding the probability of not knowing this symbol.

Step 2: Recall the complement rule in probability. The complement rule states that the probability of an event not occurring is equal to 1 minus the probability of the event occurring. Mathematically, this is expressed as: P(not A) = 1 - P(A).

Step 3: Substitute the given probability into the complement formula. Here, P(A) = 0.13, so P(not A) = 1 - 0.13.

Step 4: Perform the subtraction to find the probability of not knowing the symbol. This will give you the value of P(not A).

Step 5: Interpret the result. The final value represents the probability of randomly selecting an adult in the U.S. who does not know the care-instruction symbol for any bleach.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it helps determine the chance of randomly selecting an adult who does not know the care-instruction symbol for bleach usage. The probability can be calculated by subtracting the known percentage from 100%.

Complementary Events

Complementary events are pairs of outcomes in a probability scenario where one event occurs if and only if the other does not. In this case, knowing the percentage of adults who understand the symbol allows us to find the complementary percentage of those who do not, which is essential for calculating the desired probability.

Random Sampling

Random sampling is a technique used to select a subset of individuals from a larger population, ensuring that each member has an equal chance of being chosen. This concept is crucial for the question as it assumes that the selected adult is representative of the entire U.S. adult population, allowing for valid probability calculations.

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