The table gives the results of a survey of 219,864...

The table gives the results of a survey of $219,864$ first-year shudents from the class of 2013 at 297 of the nation's four-year colleges and universities.$$\begin{array}{|l|c|c|c|c}\hline \text { Number of Colleges Applied to } & 1 & 2 \text { or } 3 & 4-6 & 7 \text { or more } \\\hline \text { Percent (as a decimal) } & 0.14 & 0.24 & 0.39 & 0.23 \\\hline\end{array}$$ Using the percents as probabilities, find the probability of each event for a randomly selected student. The student applied to fewer than

The table gives the results of a survey of $219,864$ first-year shudents from the class of 2013 at 297 of the nation's four-year colleges and universities.$$\begin{array}{|l|c|c|c|c}\hline \text { Number of Colleges Applied to } & 1 & 2 \text { or } 3 & 4-6 & 7 \text { or more } \\\hline \text { Percent (as a decimal) } & 0.14 & 0.24 & 0.39 & 0.23 \\\hline\end{array}$$
Using the percents as probabilities, find the probability of each event for a randomly selected student.
The student applied to fewer than

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Key Concepts

Cumulative Probability

When determining the probability of a compound event such as 'fewer than a given number of colleges applied to', cumulative probability is used. This involves summing the probabilities of all individual events that meet the criterion to find the total probability.

Combined Events

This key concept refers to the evaluation of probabilities for a union of several outcomes. For example, if assessing the likelihood that a student applied to fewer than a certain number of colleges, one must add together the probabilities of each distinct outcome that satisfies this condition.

Relative Frequency Probability

This concept involves using the proportions or percentages from survey data as probabilities. Each percentage, when expressed as a decimal, represents the likelihood of a randomly selected student falling into a particular category.

Discrete Probability Distribution

The table presents a discrete probability distribution where each outcome (number of colleges applied to) has an associated probability. This distribution shows how the probabilities are assigned to mutually exclusive events in the survey.

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