# Séminaire de Probabilités VII

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An order for an automobile can specify either an automatic or a standard transmission, either with or without air conditioning, and with any one of the four colors red, blue, black, or white. Describe the set of possible orders for this experiment. 2-15. A sampled injection-molded part could have been produced in either one of two presses and in any one of the eight cavities in each press. 2-16. An order for a computer system can specify memory of 4, 8, or 12 gigabytes and disk storage of 200, 300, or 400 gigabytes.

B) If the first bit of a byte is a parity check, that is, the first byte is determined from the other seven bits, how many different bytes are possible? 2-47. In a chemical plant, 24 holding tanks are used for final product storage. Four tanks are selected at random and without replacement. Suppose that six of the tanks contain material in which the viscosity exceeds the customer requirements. (a) What is the probability that exactly one tank in the sample contains high-viscosity material? (b) What is the probability that at least one tank in the sample contains high-viscosity material?

For example, if the set is S = {a, b, c, d}, the subset {a, c} can be indicated as a b c d * ∗ Combinations The number of combinations, subsets of r elements that can be selected from a set of n elements, is denoted as rn or Crn and () ⎛ n⎞ n! ( n − r )! Example 2-13 (2-4) Printed Circuit Board Layout A printed circuit board has eight different locations in which a component can be placed. If five identical components are to be placed on the board, how many different designs are possible? Each design is a subset of size five from the eight locations that are to contain the components.