In planning the operation of a new school, one schoolboard member claims that four out of five newly hiredteachers will stay with the school for more than a year,while another school board member claims that it wouldbe correct to say three out of five. In the past, the twoboard members have been about equally reliable in theirpredictions, so in the absence of any other informationwe would assign their judgments equal weight. If oneor the other has to be right, what probabilities wouldwe assign to their claims if it were found that 11 of 12newly hired teachers stayed with the school for more thana year?
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.
In planning the operation of a new school, one school
board member claims that four out of five newly hired
teachers will stay with the school for more than a year,
while another school board member claims that it would
be correct to say three out of five. In the past, the two
board members have been about equally reliable in their
predictions, so in the absence of any other information
we would assign their judgments equal weight. If one
or the other has to be right, what probabilities would
we assign to their claims if it were found that 11 of 12
newly hired teachers stayed with the school for more than
a year?
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