At the beginning of the semester, a professor tells students that if they study for the tests, then there is a 55% chance they will get a B or higher on the tests. If they do not study, there is a 20% chance that they will get a B or higher on the tests. The professor knows from prior surveys that 60% of students study for the tests. The probabilities are displayed in the tree diagram.The professor informs the class that there will be a test next week. What is the probability that a randomly selected student studied for the test if they pass it with a B or higher?0.200.550.600.80 The diagram is a decision tree that illustrates the probability of a student's performance on a test based on whether or not they study.1. **Initial Node (Random student):** - The process starts with a "Random student."2. **First Branch:** - **Studies for test**: There is a 60% (0.6) probability that the student studies for the test. - **Does not study for test**: There is a 40% (0.4) probability that the student does not study for the test.3. **Outcomes if Student Studies:** - **Gets B or higher**: There is a 55% (0.55) probability that a student who studies will get a B or higher. - **Does not get B or higher**: There is a 45% (0.45) probability that a student who studies will not get a B or higher.4. **Outcomes if Student Does Not Study:** - **Gets B or higher**: There is a 20% (0.20) probability that a student who does not study will get a B or higher. - **Does not get B or higher**: There is an 80% (0.80) probability that a student who does not study will not get a B or higher.This decision tree can help visualize the impact of studying on academic performance and assess the risks associated with different levels of preparation.

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professor tells students that if they study for the tests, then there is a 55% chance they will get a B or higher on the tests. If they do not study, there is a 20% chance that they will get a B or higher on the tests. The professor knows from prior surveys that 60% of students study for the tests. The probabilities are displayed in the tree diagram. The professor informs the class that there will be a test next week. What is the probability that a randomly selected student studied for the test if they pass it with a B or higher? 0.20 0.55 0.60 0.80

professor tells students that if they study for the tests, then there is a 55% chance they will get a B or higher on the tests. If they do not study, there is a 20% chance that they will get a B or higher on the tests. The professor knows from prior surveys that 60% of students study for the tests. The probabilities are displayed in the tree diagram. The professor informs the class that there will be a test next week. What is the probability that a randomly selected student studied for the test if they pass it with a B or higher? 0.20 0.55 0.60 0.80

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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Question

At the beginning of the semester, a professor tells students that if they study for the tests, then there is a 55% chance they will get a B or higher on the tests. If they do not study, there is a 20% chance that they will get a B or higher on the tests. The professor knows from prior surveys that 60% of students study for the tests. The probabilities are displayed in the tree diagram.

The professor informs the class that there will be a test next week. What is the probability that a randomly selected student studied for the test if they pass it with a B or higher?

0.20

0.55

0.60

0.80

The diagram is a decision tree that illustrates the probability of a student's performance on a test based on whether or not they study.

1. **Initial Node (Random student):**
- The process starts with a "Random student."

2. **First Branch:**
- **Studies for test**: There is a 60% (0.6) probability that the student studies for the test.
- **Does not study for test**: There is a 40% (0.4) probability that the student does not study for the test.

3. **Outcomes if Student Studies:**
- **Gets B or higher**: There is a 55% (0.55) probability that a student who studies will get a B or higher.
- **Does not get B or higher**: There is a 45% (0.45) probability that a student who studies will not get a B or higher.

4. **Outcomes if Student Does Not Study:**
- **Gets B or higher**: There is a 20% (0.20) probability that a student who does not study will get a B or higher.
- **Does not get B or higher**: There is an 80% (0.80) probability that a student who does not study will not get a B or higher.

This decision tree can help visualize the impact of studying on academic performance and assess the risks associated with different levels of preparation.

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