In the work force of a large factory, 70 % of the employees...

In the work force of a large factory, $70 \%$ of the employees are high-school graduates, $8 \%$ are supervisors, and $5 \%$ are both supervisors and high-school graduates. From this information, answer these questions. (a) If the employee is a high-school graduate, what is the probability he is a supervisor? (b) If the employee is not a high-school graduate, what is the probability be is a supervisor?

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Key Concepts

Conditional Probability

This concept is used to determine the likelihood of one event occurring under the condition that another event has already occurred. It is expressed as the ratio of the probability of the intersection of the events to the probability of the conditioning event, which is critical when evaluating scenarios that depend on given conditions.

Intersection of Events

This refers to the scenario where two events occur simultaneously. Calculating the probability of the intersection helps in understanding how often two characteristics or conditions overlap, which is necessary for computing conditional probabilities.

Complementary Events

This concept involves events that are mutually exclusive and together cover the entire sample space. In probability, the idea of a complementary event is used to calculate the likelihood of an event not occurring by subtracting the probability of the event from one, which is useful in determining probabilities within subsets of a population.

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