Texting and Driving. In Exercises 21–26, refer to the accompanying table, which describes probabilities for groups of five drivers. The random variable x is the number of drivers in a group who say that they text while driving (based on data from an Arity survey of drivers).

Using Probabilities for Significant Events

b. Find the probability of getting 3 or more drivers who say that they text while driving.

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Step 1: Understand the problem. We are tasked with finding the probability of getting 3 or more drivers who say they text while driving. This means we need to calculate P(x ≥ 3), where x is the number of drivers in a group who text while driving.

Step 2: Use the complement rule to simplify the calculation. The complement of P(x ≥ 3) is P(x < 3). Therefore, P(x ≥ 3) = 1 - P(x < 3).

Step 3: Calculate P(x < 3) by summing the probabilities for x = 0, x = 1, and x = 2. From the table, these probabilities are P(0) = 0.066, P(1) = 0.238, and P(2) = 0.344.

Step 4: Add the probabilities for x = 0, x = 1, and x = 2 to find P(x < 3). This will give the total probability of having fewer than 3 drivers who text while driving.

Step 5: Subtract P(x < 3) from 1 to find P(x ≥ 3). This will give the probability of having 3 or more drivers who text while driving.

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주요 개념

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Random Variable

A random variable is a numerical outcome of a random phenomenon. In this context, the random variable x represents the number of drivers in a group of five who report texting while driving. Understanding random variables is crucial for analyzing probabilities and making inferences about populations based on sample data.

Probability Distribution

A probability distribution describes how probabilities are assigned to each possible value of a random variable. The table provided shows the probability distribution for the random variable x, indicating the likelihood of 0 to 5 drivers texting while driving. This distribution is essential for calculating probabilities of specific outcomes, such as finding the probability of 3 or more drivers texting.

Cumulative Probability

Cumulative probability refers to the probability that a random variable takes on a value less than or equal to a certain number. To find the probability of getting 3 or more drivers who text while driving, one must calculate the cumulative probabilities for 0, 1, and 2 drivers and subtract this sum from 1. This concept is vital for understanding how to aggregate probabilities for ranges of outcomes.