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Chapter 1: Problem 7

A student entering a doctoral program in educational psychology is required to select two courses from the list of courses provided as part of his or her program. EPR 616, Research in Child Development EPR 630, Educational Research Planning and Interpretation EPR 631, Nonparametric Statistics EPR 632, Methods of Multivariate Analysis EPR 645, Theory of Measurement EPR 649, Fieldwork Methods in Educational Research EPR \(650,\) Interpretive Methods in Educational Research (a) List all possible two-course selections. (b) Comment on the likelihood that the pair of courses EPR 630 and EPR 645 will be selected.

Short Answer

Expert verified
All possible pairs: 21. Probability of selecting EPR 630 and EPR 645: \( \frac{1}{21} \).

Step by step solution

01

Identify the Courses

List all available courses: EPR 616, EPR 630, EPR 631, EPR 632, EPR 645, EPR 649, EPR 650.
02

Determine Total Pairs

Use the combinations formula to calculate the total number of ways to select 2 courses out of 7. The formula is \(\binom{n}{k}\), where \(n\) is the total number of courses, and \(k\) is the number of courses to select: \(\binom{7}{2} = \frac{7!}{2!(7-2)!} = 21\).
03

List All Possible Combinations

List all combinations of two courses from the provided courses: 1. EPR 616 and EPR 6302. EPR 616 and EPR 6313. EPR 616 and EPR 6324. EPR 616 and EPR 6455. EPR 616 and EPR 6496. EPR 616 and EPR 6507. EPR 630 and EPR 6318. EPR 630 and EPR 6329. EPR 630 and EPR 64510. EPR 630 and EPR 64911. EPR 630 and EPR 65012. EPR 631 and EPR 63213. EPR 631 and EPR 64514. EPR 631 and EPR 64915. EPR 631 and EPR 65016. EPR 632 and EPR 64517. EPR 632 and EPR 64918. EPR 632 and EPR 65019. EPR 645 and EPR 64920. EPR 645 and EPR 65021. EPR 649 and EPR 650
04

Determine Likelihood of Specific Pair

Calculate the likelihood that the pair EPR 630 and EPR 645 will be selected. Since all pairs are equally possible and there are 21 pairs, the likelihood is \( \frac{1}{21} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

combinatorial mathematics
Combinatorial mathematics helps us understand how to count combinations. In this exercise, we used it to find the number of possible combinations of two courses out of seven. The formula for combinations is given by: \(\binom{n}{k} = \frac{n!}{k!(n - k)!} \). This formula tells us how many ways we can choose k items from n items without considering the order. For instance, in our exercise, n = 7 (total courses) and k = 2 (courses selected), so we calculate: \[\binom{7}{2} = \frac{7!}{2!(7-2)!} = 21 \]. This means there are 21 ways to select two courses out of seven, each combination being unique.
probability
Probability is the measure of how likely an event is to occur. We used probability to find out how likely it is for a specific pair of courses, like EPR 630 and EPR 645, to be selected from the list. Since we already know there are 21 possible combinations, and each combination is equally likely to be chosen, the probability of selecting any specific pair, including EPR 630 and EPR 645, is: \(\frac{1}{21} \). This fraction means there's a one in 21 chance of selecting that pair if the selection is made randomly. Understanding this concept helps students appreciate how often certain outcomes can occur.
doctoral education
In the context of doctoral education, students must make critical decisions about their course selections. Particularly in a program like educational psychology, selecting courses helps shape their academic and professional future. Choosing the right courses can lead to a strong foundation for their research interests and career goals. For instance, courses like EPR 616 and EPR 645 might provide a student with comprehensive research skills. Doctoral programs often encourage students to balance their courses between required subjects and those that align with their specific research interests. Making informed choices is key to success in a doctoral journey.

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