A recent study concerning knee injuries of football players compared two types of football shoes. Out of a randomly chosen group of 1440 players, 240 used multicleated shoes and $200 used more conventional football shoes. All played on natural grass. Of those using the multicleated shoes, 13 suffered knee injuries. Of those using conventional shoes, 78 suffered knee injuries. (a) Test the hypothesis that the probability of a knee injury is the same for both groups of players. Use the 5 percent level of significance. (b) Are the given data strong enough to establish that the multicleated shoes are superior to the conventional ones in terms of reducing the probability of a knee injury? (c) In part (b), at what levels of significance would the evidence be strong enough?
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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