A traffic cop has been determined that (7 %) of drivers checked to use their mobile phones and ((13) %) of drivers checked do not wear seat belts. In addition, it has been observed that the two infractions are independent from one another. If the cop stops seven drivers at random: a. Calculate the probability that exactly five of the drivers have committed any one of the two offenses. b. Calculate the probability that at least one of the drivers checked has committed at least one of the two offenses.
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.
A traffic cop has been determined that (7 %) of drivers checked to use their mobile phones and ((13) %) of drivers checked do not wear seat belts. In addition, it has been observed that the two infractions are independent from one another. If the cop stops seven drivers at random:
a. Calculate the probability that exactly five of the drivers have committed any one of the two offenses.
b. Calculate the probability that at least one of the drivers checked has committed at least one of the two offenses.
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