PROBABILITY AND STATISTICS

PROBLEM 1.

Probability theory and statistical techniques make important contributions to the space program. In this chapter we examine the role of probability in menu planning, in some aspects of the transmission and coding of spacecraft observations, and in the control of equipment reliability. Some elementary examples of the use of statistics are illustrated in the final two problems.

PROBLEM 1.The early manned spaceflights revealed much about the body's response to prolonged weightlessness. An interesting and varied food supply was thus needed to guard against a loss of appetite in the face of what was learned. The food supply for the crew of the Space Shuttle is carefully planned to compensate for the high energy requirements (averaging 3000 calories per person per day) of working in a frictionless environment and the body's tendency to lose essential minerals (such as potassium, calcium, and nitrogen) in microgravity. The Space Shuttle food and beverage list contains more than a hundred individual items. A typical day's menu might be the following:

In general, each meal III contains a main dish, a vegetable, and two desserts, with an appetizer included every other day. The food list contains 10 items classified as main dishes (M), 8 vegetable dishes (V), 13 desserts (D), and 3 appetizers (A). How many different menu combinations are possible in each of the first six days of flight, assuming no dish is repeated?

Solution: The number of choices is tabulated below:

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