3. Three energy drink distributers, A, B, and C, currently 20%, 30%, and 50% of the market, respectively. Each wants to increase its share of the market, and to do so, each introduces a new brand. During the next year, it is learned that: • A loses 20% of its business to B and 30% to C. • B loses 40% of its business to A and 20% to C. • Closes 50% of its business to A and 25% to B. a. Create a transition diagram b. Write the transition matrix C. If this trend continues, what share does each distributor have after 5 years? Show the initial matrices, the notation for what you are calculating, and the final matrix as a result (you may use your calculator!). Give a one-sentence interpretation of the result.
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.
Tree diagram
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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