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Fill in the table below to complete the probability density function. Be certain to list the values of X in ascending order. Value of X Probability 12/21 3/21

Fill in the table below to complete the probability density function. Be certain to list the values of X in ascending order. Value of X Probability 12/21 3/21

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Can someone please help me figure out the probability portion of this question?

**Reworking Problem 5 - Section 4.2** **Context:** Consider the problem of selecting two students randomly from a committee comprising six members—four males and two females. The task is to determine the number of males selected, defined as the random variable \( X \). **1. Number of Possible Values for \( X \):** - The random variable \( X \) can take on three different values, which are the number of males that could be selected in the two-student sample. **2. Values of \( X \) and Their Probabilities:** Below is the probability density function table that outlines each possible value of \( X \) and the corresponding probability. | **Value of \( X \)** | **Probability** | |--------------------|-----------------| | 0 | 0 | | 1 | \(\frac{12}{21}\) | | 2 | \(\frac{3}{21}\) | **Notes:** - The table lists the values of \( X \) in ascending order. - It's crucial to understand that the probability of \( X = 0 \) is zero, meaning it's impossible to select two females since there are only two females in the group, and we're selecting two students. - The majority probability occurs when one male and one female are selected, corresponding to \( X = 1 \). - The calculations involved in understanding these probabilities require combinatorial reasoning, such as determining the number of ways to choose males and females from the committee. This setup helps students grasp basic probability concepts and apply them to scenarios involving sample selections from small groups.
Transcribed Image Text:**Reworking Problem 5 - Section 4.2** **Context:** Consider the problem of selecting two students randomly from a committee comprising six members—four males and two females. The task is to determine the number of males selected, defined as the random variable \( X \). **1. Number of Possible Values for \( X \):** - The random variable \( X \) can take on three different values, which are the number of males that could be selected in the two-student sample. **2. Values of \( X \) and Their Probabilities:** Below is the probability density function table that outlines each possible value of \( X \) and the corresponding probability. | **Value of \( X \)** | **Probability** | |--------------------|-----------------| | 0 | 0 | | 1 | \(\frac{12}{21}\) | | 2 | \(\frac{3}{21}\) | **Notes:** - The table lists the values of \( X \) in ascending order. - It's crucial to understand that the probability of \( X = 0 \) is zero, meaning it's impossible to select two females since there are only two females in the group, and we're selecting two students. - The majority probability occurs when one male and one female are selected, corresponding to \( X = 1 \). - The calculations involved in understanding these probabilities require combinatorial reasoning, such as determining the number of ways to choose males and females from the committee. This setup helps students grasp basic probability concepts and apply them to scenarios involving sample selections from small groups.
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