A mail-order house employs three stock clerks, U,V, and W, who pull items from shelves and assemblethem for subsequent verification and packaging. U makesa mistake in an order (gets a wrong item or the wrongquantity) one time in a hundred, V makes a mistake inan order five times in a hundred, and W makes a mistakein an order three times in a hundred. If U, V, and W fill,respectively, 30, 40, and 30 percent of all orders, what arethe probabilities that(a) a mistake will be made in an order;(b) if a mistake is made in an order, the order was filledby U;(c) if a mistake is made in an order, the order was filledby V?
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 mail-order house employs three stock clerks, U,
V, and W, who pull items from shelves and assemble
them for subsequent verification and packaging. U makes
a mistake in an order (gets a wrong item or the wrong
quantity) one time in a hundred, V makes a mistake in
an order five times in a hundred, and W makes a mistake
in an order three times in a hundred. If U, V, and W fill,
respectively, 30, 40, and 30 percent of all orders, what are
the
(a) a mistake will be made in an order;
(b) if a mistake is made in an order, the order was filled
by U;
(c) if a mistake is made in an order, the order was filled
by V?
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