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Records of a Company Show That 15% of the Employees

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Records of a company show that 15% of the employees have only a high school diploma; 75% have bachelor degrees; and 10% have graduate degrees. Of those with only a high school diploma, 12% hold management positions; whereas, of those having bachelor degrees, 58% hold management positions. Finally, 82% of the employees who have graduate degrees hold management positions.
a.What percentage of employees holds management positions?
b.Given that a person holds a management position, what is the probability that she/he has a graduate degree?

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Definitions:

Lewis Structure

A representation of the distribution of electrons in molecules, illustrating how the valence electrons are arranged among the atoms in the molecule.

Methane

A simple hydrocarbon with the formula CH4, it is the main component of natural gas and a potent greenhouse gas.

Lewis Structure

A graphical representation of the electron distribution around atoms and the chemical bonds that hold the atoms together.

Water

A transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of most living organisms.

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