2. You manage a company that purchases movie theaters. You have a spending goal of $4, 300 million for the purchase of new theaters to seat a total of 4,980 guests. You are given the following data: ABC theaters seat a total of 330 guests and cost $250 million each, CineMovie theaters seat 270 guests and cost $200 million each, and Movies 'n' Stuff theaters seat 240 guests and cost $250 million each. Your company wants you to buy half as many ABC theaters as the combined total of CineMovie and Movies 'n' Stuff theaters. You are tasked with determining how many of each theater your company should purchase. (a) Define variables and determine the constraints associated with this problem. Use them to set up a system of linear equations that models this scenario. (b) After applying Gauss-Jordan reduction, you arrive at the following augmented matrix: T10 0 6 Io 1 04 0 018 How many of each theater should your company purchase?
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
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