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Chapter 7: Problem 14

The results of a recent television survey of American TV households revealed that 87 out of every 100 TV households have at least one remote control. What is the probability that a randomly selected TV household does not have at least one remote control?

Short Answer

Expert verified
The probability that a randomly selected TV household does not have at least one remote control is \(\frac{13}{100}\) or 13%.

Step by step solution

01

Understand the given information

We are given that 87 out of every 100 TV households have at least one remote control. This can be represented as a proportion by dividing the number of households with at least one remote control (87) by the total number of households (100).
02

Calculate the proportion of households with at least one remote control

The proportion of households with at least one remote control can be calculated as: \[\frac{87}{100}\]
03

Find the complement of the proportion

The complement of a proportion is the remaining part that makes it equal to 1. In other words, it's the probability of the opposite event occurring. In this case, we want to find the probability of a TV household not having at least one remote control. To find the complement, subtract the proportion with at least one remote control from 1: \[1 - \frac{87}{100}\]
04

Calculate the probability of not having at least one remote control

Now calculate the result: \[1 - \frac{87}{100} = \frac{13}{100}\] So the probability that a randomly selected TV household does not have at least one remote control is \(\frac{13}{100}\) or 13%.

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Most popular questions from this chapter

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