The image depicts a Venn diagram within a rectangular box. The Venn diagram consists of two overlapping circles.1. **Art Circle**: The left circle is labeled "Art" and contains the number 6, indicating that there are 6 students exclusively involved in art.2. **Band Circle**: The right circle is labeled "Band" and contains the number 7, representing 7 students exclusively involved in band.3. **Overlap**: The overlapping area of the two circles contains the number 10, indicating that there are 10 students involved in both art and band.4. **Outside the Circles**: The number 3 is located outside both circles, inside the rectangle, representing 3 students who are neither in art nor in band.This diagram is useful for visually representing the distribution and overlap of student involvement in art and band activities. c) What is the probability that a student is not taking either class?

From the given Venn diagram, it is observed that the number of students who are taking art only is…

Answered: What is the Probability that a student…

Math

Advanced Math

What is the Probability that a student is not taking either class?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

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.

Question

The image depicts a Venn diagram within a rectangular box. The Venn diagram consists of two overlapping circles.

1. **Art Circle**: The left circle is labeled "Art" and contains the number 6, indicating that there are 6 students exclusively involved in art.

2. **Band Circle**: The right circle is labeled "Band" and contains the number 7, representing 7 students exclusively involved in band.

3. **Overlap**: The overlapping area of the two circles contains the number 10, indicating that there are 10 students involved in both art and band.

4. **Outside the Circles**: The number 3 is located outside both circles, inside the rectangle, representing 3 students who are neither in art nor in band.

This diagram is useful for visually representing the distribution and overlap of student involvement in art and band activities.

c) What is the probability that a student is not taking either class?

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