# Conditional Probabilities

The Caterpillar Corporation depicts the current status for various classifications of equipment used in a Caterpillar manufacturing plant. The company categorizes equipment usage as Low, Medium, or High, depending upon the number of expected manufacturing applications applicable to its use. Equipment is also subject to availability, depending upon its current condition for usage. The plant considers two categories for suitability for use as: In Working Order, and Under Repair. The plant maintains complete status records for all equipment categories in order to schedule production. Currently, records indicate that 10, 18, and 12 pieces of equipment in Low, Moderate, and High usage categories, respectively are available as In Working Order condition. Similarly, 2, 6, and 8 pieces of equipment in Low, Moderate, and High usage categories, respectively are included in the Under Repair condition.

a. Determine the probability that a randomly selected piece of equipment is a high usage item given that it is in working order.

b. Determine the probability that a randomly selected piece of equipment is under repair given that it is a moderate use item.

c. Determine the probability that a randomly selected piece of equipment is in working order. Determine the probability that a randomly selected piece of equipment is in working order given that it is a low usage item. Explain the difference.

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The solution provides step by step method for the calculation of probabilities and conditional probabilities. Formula for the calculation and Interpretations of the results are also included.