A Recent Survey Was Conducted Of The 30 Largest Public Compa

A Recent Survey Was Conducted Of The 30largest Public Companies In A P

A recent survey was conducted of the 30 largest public companies in a particular country. Of these 30 companies, 6 were banking or investment companies based in city X. A total of 12 city X companies were on the top 30 list. Suppose we select one of these 30 companies at random. Given that the company is based in city X, what is the probability that it is a banking or investment company? (Round to three decimal places as needed.)

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The probability that a company is a banking or investment company given that it is based in city X can be calculated using conditional probability. Specifically, we are interested in P(Banking | City X), which is the probability that the company is a banking or investment firm given that it is located in city X. Using the formula for conditional probability: P(Banking | City X) = P(Banking and City X) / P(City X).

From the survey data, we know that:

  • Total companies in the top 30: 30
  • Companies based in city X: 12
  • Banking or investment companies based in city X: 6

Assuming that the companies are uniformly distributed among the top 30 and the subset based in city X, the probability that a randomly selected company from the top 30 is both a banking or investment firm and based in city X is the number of such firms divided by the total number of companies, which is 6/30.

Similarly, the probability that a company is based in city X is 12/30. Therefore, the conditional probability is calculated as:

P(Banking | City X) = (Number of banking/investment companies in city X) / (Total companies in city X) = 6 / 12 = 0.5.

Thus, the probability that a company is a banking or investment company given that it is based in city X is 0.5. Rounded to three decimal places, this probability is 0.500.

In conclusion, the data indicates that, within city X, there is a 50% chance that a company is a banking or investment firm, highlighting the significant presence of banking institutions in that city among the largest public companies.

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