The management of Mark's Department Store estimates that approximately 2% of all shoppers enter the store with the intention of shoplifting. Of those people who engage in the act of shoplifting, 94% are apprehended by security guards using closed-circuit television (CCTV) and an electronic article surveillance system. The latter, also called a tag-and-alarm system, involves the use of a tag or label that is attached to an item. The tag is deactivated or detached at the time of purchase of the item; failure to do so will trigger an alarm when the item is carried through the gates. Of the other 98% of the shoppers, 1% are mistakenly identified as shoplifters by security guards watching them on CCTV or have triggered the alarm because the salesperson failed to deactivate or detach the tag. If a shopper is detained by security, what is the probability that the person was in fact a shoplifter? (Round your answer to two decimal places.
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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