Figures obtained from a city’s police department seem to indicate that, of all motor vehicles reported as stolen, 64% were stolen by professionals, 36% were stolen by amateurs (primarily for joy rides). Of those stolen by professionals, 24% were recovered within 48 hr, 16% were recovered after 48 hr and 60% were never recovered. Of those vehicles presumed stolen by amateurs, 38% were recovered within 48 hr, 58% were recovered after 48 hr and 4% were never recovered. a) Draw a tree diagram representing the situation. b) What is the probability that a vehicle stolen by a professional in this city and will be recovered within 48 hr? c) What is the probability that a vehicle stolen in this city will never be recovered?
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.
Figures obtained from a city’s police department seem to indicate that, of all motor vehicles reported as stolen,
64% were stolen by professionals, 36% were stolen by amateurs (primarily for joy rides). Of those stolen by
professionals, 24% were recovered within 48 hr, 16% were recovered after 48 hr and 60% were never recovered.
Of those vehicles presumed stolen by amateurs, 38% were recovered within 48 hr, 58% were recovered after 48 hr
and 4% were never recovered.
a) Draw a tree diagram representing the situation.
b) What is the probability that a vehicle stolen by a professional in this city and will be recovered within 48 hr?
c) What is the probability that a vehicle stolen in this city will never be recovered?
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