Question

A Nielsen survey of teens between the ages of 13 and 17 found that \(83 \%\) use text messaging and \(56 \%\) use picture messaging (“How Teens Use Media," Nielsen, June 2009). Use these percentages to explain why the two events \(T=\) event that a randomly selected teen uses text messaging and \(P=\) event that a randomly selected teen uses picture messaging cannot be mutually exclusive.

Short answer

The events T (text messaging) and P (picture messaging) cannot be mutually exclusive because their combined probability exceeds 100%, meaning it's possible for a teen to do both.

Step-by-step solution

Understanding Mutually Exclusive Events

Mutually exclusive events are those where if one event occurs, the other cannot. For instance, when flipping a coin, getting a head and getting a tail are mutually exclusive events because you can't get both at the same time.

Analyzing the Scenario

In this case, the event T (that a randomly selected teen uses text messaging, 83%) and the event P (that a randomly selected teen uses picture messaging, 56%) are the probabilities given.

Sum of Probabilities

Summing up the probabilities of the two events, we get \(83% + 56% = 139%\).

Interpretation

The sum of the probabilities of the events (139%) is more than 100% which implies that a randomly selected teen may engage in both activities (text and picture messaging). Hence, the two events T and P cannot be mutually exclusive.

Key concepts

Understanding Probability

Probability is the branch of mathematics that deals with measuring the likelihood of the occurrence of an event. It is represented as a number between 0 and 1, where 0 implies that the event is impossible to occur, and 1 indicates that the event is certain to happen. In between values express the level of uncertainty associated with the event.

When we look at surveys like the Nielsen survey mentioned in our exercise, we can use probability to express how common certain behaviors are among a group, such as teenagers. If 83% of teens use text messaging, we can interpret this as the probability of selecting a teen at random who uses text messaging is 0.83 or \(83\%\).

In a real-world scenario, probabilities help in making predictions, assessments, and decisions based on the likelihood of various outcomes. The understanding of how to calculate and interpret probabilities is crucial for statistics and is widely applicable in fields such as science, engineering, economics, and social sciences.

Text Messaging Usage Among Teens

Text messaging usage refers to the frequency or the proportion of individuals who use SMS or texting services to communicate. In the context of the survey result which shows that 83% of teens between the ages of 13 and 17 text, it highlights that texting is a prevalent mode of communication in this age group.

For educators and content creators, it's important to recognize that data on text messaging usage can be indicative of larger social and communication trends. Additionally, such information can also relate to technology adaptation rates, cultural shifts, and even language evolution as text messaging often involves its own set of linguistic shortcuts and conventions.

When considering teenagers in particular, these statistics also provide insights into how education, marketing, and policy might be shaped to accommodate the communication preferences of younger generations. It guides stakeholders in creating approaches that align with the desires and habits of their intended audience.

Picture Messaging Usage Among Teens

Picture messaging, also known as MMS (Multimedia Messaging Service), is another form of digital communication which includes the sending of images, videos, and audio content. According to the Nielsen survey, 56% of teens engage in picture messaging, showcasing a significant adoption of multimedia communication at a young age.

This statistic not only informs us about the sheer volume of teens involved in this form of communication, but also raises questions about the impact of visual content on teen interaction, socialization, and even education. With picture messaging, teens are engaging each other in a richer, more visually oriented context, which could have implications for their cognitive processing and preference for visual learning experiences.

Content creators should take note of this shift towards visual media consumption as it may influence the way educational and informational content is produced and delivered to meet the evolving preferences of a digitally-savvy teenage audience.