Fortune magazine publishes an annual issue containing info on Fortune 500 companies.

The following data show the six states with the largest number of Fortune 500 companies as well as the number of companies headquartered in those states.

State # of Companies
New York 56
California 53
Texas 43
Illinois 37
Ohio 28
Pennsylvania 28

Suppose a fortune 500 company is chosen for a follow up questionaire. What are the probabilities of the following events.

a. Let N be the event the company is headquartered in New York. Find P(N).
b.Headquartered in Texas. Find P(T).
c.Headquartered in one of these six states. Find P(B).

the books answers are....
a. .112
b. .086
c. .49

How are the getting these answers?

You must have omitted some additional information, such as 49% of all companies are located in these 6 states, a fact demonstrated by their answer to c.

You can verify this by doing a)

P(New York)= 56/245 *49% = .112

answers:

New York, P(x=N)= 56/500=.112

P(x=T)=43/500 = .086

P(x>=1)=P(x=N)+P(x=C)+P(x=T)+P(x=I)+P(x=O)P(x=P).
=56/500+53/500...28/500=0.49

To calculate the probabilities, we need to know the total number of Fortune 500 companies, as well as the percentage of companies that are headquartered in these six states.

Let's assume that the total number of Fortune 500 companies is 500 (as suggested by the name).

a. To find the probability of a company being headquartered in New York (P(N)), we divide the number of companies headquartered in New York (56) by the total number of companies (500).

P(N) = 56/500 = 0.112 or 11.2%

b. To find the probability of a company being headquartered in Texas (P(T)), we divide the number of companies headquartered in Texas (43) by the total number of companies (500).

P(T) = 43/500 = 0.086 or 8.6%

c. To find the probability of a company being headquartered in one of these six states (P(B)), we need to know the percentage of companies that are located in these states.

Since the book's answer is 49%, we can infer that 49% of all Fortune 500 companies are located in these six states. Therefore, P(B) = 0.49 or 49%.

To calculate the probabilities, we need to consider the total number of companies in the Fortune 500 list, which is not provided in the given information. However, you mentioned that the book's answer for part (c) indicates that 49% of all companies are located in these six states.

Using this additional information, we can proceed with the calculations as follows:

a. Probabilty of a company being headquartered in New York (P(N)):

The number of companies headquartered in New York is given as 56. Assuming the total number of companies in the Fortune 500 list is 245, we can calculate P(N) as follows:

P(N) = Number of New York companies / Total number of companies * Percentage of companies in these 6 states
= 56 / 245 * 49%
= 0.112 (or 11.2%)

b. Probability of a company being headquartered in Texas (P(T)):

The number of companies headquartered in Texas is given as 43. Using the same assumption for the total number of companies, we can calculate P(T) as follows:

P(T) = Number of Texas companies / Total number of companies * Percentage of companies in these 6 states
= 43 / 245 * 49%
= 0.086 (or 8.6%)

c. Probability of a company being headquartered in one of these six states (P(B)):

The total number of companies in the Fortune 500 list is not provided, but the book's answer indicates that 49% of all companies are located in these six states. So, we can calculate P(B) as follows:

P(B) = Percentage of companies in these 6 states
= 49%
= 0.49 (or 49%)

It's important to note that these calculations are based on the assumption mentioned earlier about the percentage of companies in these six states. Without the total number of companies in the Fortune 500 list, it is not possible to calculate the exact probabilities.