Honor Roll Yes No 9th Grade 72 120 10th Grade 95 117 11th Grade 76 124 12th Grade 57 139 P(9th grader | not honor roll)
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
![## Honor Roll Participation by Grade
Below is a table depicting the number of students in various grades who are either on the Honor Roll or not on the Honor Roll.
| Grade Level | Honor Roll (Yes) | Honor Roll (No) |
|-------------|-------------------|-----------------|
| 9th Grade | 72 | 120 |
| 10th Grade | 95 | 117 |
| 11th Grade | 76 | 124 |
| 12th Grade | 57 | 139 |
From the table, we can derive insights into the distribution of students across different grades with respect to their Honor Roll status.
**Question:**
Calculate the probability that a student is a 9th grader given that they are not on the Honor Roll:
\[ P(\text{9th grader} | \text{not honor roll}) \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd23dfbce-660c-4e5f-9443-c982b7db5eab%2F09cb703f-5820-43f4-8613-d3b792294c7b%2F6dsmkb3_processed.jpeg&w=3840&q=75)
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