A survey conducted by the Segal Company of New York found that in a sample of 189 large companies, 40 offered stock options to their board members as part of their non-cash compensation packages. For small-to-mid-sized companies, 43 of the 180 surveyed indicated that they offer stock options as part of their non-cash compensation packages to their board members.**Company Size:**| Stock Options | Large | Small-to-midsized ||---------------|-------|-------------------|| Yes | 40 | 43 || No | 149 | 137 |**Explanation:**- **Large Companies:** - Out of 189 surveyed, 40 offer stock options to board members. - 149 do not offer stock options.- **Small-to-Mid-Sized Companies:** - Out of 180 surveyed, 43 offer stock options to board members. - 137 do not offer stock options.This data compares the prevalence of stock options as non-cash compensation between large and small-to-midsized companies. d. If a randomly selected company is a large company, what is the probability that it offered stock options to their board members?e. Are company size and offering stock options statistically independent?

d) From the table it is clear that, There are 369 companies. Number of large company offered stock…

Answered: If a randomly selected company is a…

If a randomly selected company is a large company, what is the probability that it offered stock options to their board members? Are company size and offering stock options statistically independent?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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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 survey conducted by the Segal Company of New York found that in a sample of 189 large companies, 40 offered stock options to their board members as part of their non-cash compensation packages. For small-to-mid-sized companies, 43 of the 180 surveyed indicated that they offer stock options as part of their non-cash compensation packages to their board members.

**Company Size:**

| Stock Options | Large | Small-to-midsized |
|---------------|-------|-------------------|
| Yes | 40 | 43 |
| No | 149 | 137 |

**Explanation:**

- **Large Companies:**
- Out of 189 surveyed, 40 offer stock options to board members.
- 149 do not offer stock options.

- **Small-to-Mid-Sized Companies:**
- Out of 180 surveyed, 43 offer stock options to board members.
- 137 do not offer stock options.

This data compares the prevalence of stock options as non-cash compensation between large and small-to-midsized companies.

d. If a randomly selected company is a large company, what is the probability that it offered stock options to their board members?

e. Are company size and offering stock options statistically independent?

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