Refer to the accompanying venn diagram. An experiment in which the three mutually exclusive events, A, B, and C form a partition of he uniform sample space S is depicted in the diagram (round your answers to three decimal places. A. Find P(D)B. Find P(B vertical line D) - the conditional probability of B given D This image displays a diagram of a rectangular region divided into three vertical sections labeled A, B, and C. Within this rectangular region, there is an ellipse centered in the middle vertical section (B) and extending partially into sections A and C. Here is a detailed breakdown of the components for better understanding:1. **Rectangular Region**: - The entire area is encapsulated in a blue rectangle. - The rectangle is divided into three vertical sections: - **A** (left section) - **B** (middle section) - **C** (right section)2. **Elliptical Region**: - An ellipse is drawn within the rectangular region with its center aligned in section B. - The ellipse overlaps partly into sections A and C.3. **Numerical Values**: - The rectangular region (excluding the ellipse) has numerical values written in red: - 35 in section A, above the ellipse. - 40 in section A, below the ellipse. - 15 in section C, below the ellipse. - The elliptical region has different numerical values written in red at four points: - 35 in section A, within the ellipse. - 40 in section B, within the ellipse (center). - 15 in section C, within the ellipse.This diagram can be used in an educational setting to illustrate how different numerical values are distributed both inside and outside of a specific sub-region (the ellipse) within a larger divided area (the rectangle). It can help students understand concepts related to set theory, probability, or partitioning of a sample space in various fields such as mathematics or statistics.

a) P(D) = n(D) / n(S) = (35 + 40 + 15) / (35+40+15+35+40+40) = 90 / 205 =…

Refer to the accompanying venn diagram. An experiment in which the three mutually exclusive events, A, B, and C form a partition of he uniform sample space S is depicted in the diagram (round your answers to three decimal places. A. Find P(D) B. Find P(B vertical line D) - the conditional probability of B given D

Refer to the accompanying venn diagram. An experiment in which the three mutually exclusive events, A, B, and C form a partition of he uniform sample space S is depicted in the diagram (round your answers to three decimal places. A. Find P(D) B. Find P(B vertical line D) - the conditional probability of B given D

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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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

A. Find P(D)

B. Find P(B vertical line D) - the conditional probability of B given D

This image displays a diagram of a rectangular region divided into three vertical sections labeled A, B, and C. Within this rectangular region, there is an ellipse centered in the middle vertical section (B) and extending partially into sections A and C.

Here is a detailed breakdown of the components for better understanding:

1. **Rectangular Region**:

- The entire area is encapsulated in a blue rectangle.
- The rectangle is divided into three vertical sections:
- **A** (left section)
- **B** (middle section)
- **C** (right section)

2. **Elliptical Region**:

- An ellipse is drawn within the rectangular region with its center aligned in section B.
- The ellipse overlaps partly into sections A and C.

3. **Numerical Values**:

- The rectangular region (excluding the ellipse) has numerical values written in red:
- 35 in section A, above the ellipse.
- 40 in section A, below the ellipse.
- 15 in section C, below the ellipse.

- The elliptical region has different numerical values written in red at four points:
- 35 in section A, within the ellipse.
- 40 in section B, within the ellipse (center).
- 15 in section C, within the ellipse.

This diagram can be used in an educational setting to illustrate how different numerical values are distributed both inside and outside of a specific sub-region (the ellipse) within a larger divided area (the rectangle). It can help students understand concepts related to set theory, probability, or partitioning of a sample space in various fields such as mathematics or statistics.

Definition Definition For any random event or experiment, the set that is formed with all the possible outcomes is called a sample space. When any random event takes place that has multiple outcomes, the possible outcomes are grouped together in a set. The sample space can be anything, from a set of vectors to real numbers.

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