In a small, local factory in the State of Washington in 2019, assembly lines #1, #2, and #3 respectively produce 15%, 30%, and 55% of all the items. Of their respective outputs, 6%, 3%, and 1% are defective. An item is selected at random from the total output of the local factory. 1 . What is the probability that it is defective? 2. Given that it is defective, what is the probability that it was made by assembly line #2?
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 a small, local factory in the State of Washington in 2019, assembly lines #1, #2, and #3 respectively produce 15%, 30%, and 55% of all the items. Of their respective outputs, 6%, 3%, and 1% are defective. An item is selected at random from the total output of the local factory.
1 . What is the
2. Given that it is defective, what is the probability that it was made by assembly line #2?
Let A be event such that assembly line #1 produces the items.
P(A) = 0.15
Let B be event such that assembly line #2 produces the items.
P(B) = 0.30
Let C be event such that assembly line #3 produces the items.
P(C) = 0.55
Let D be detective items.
P(D|A) = 0.06
P(D|B) = 0.03
P(D|C) = 0.01
We have to find the probability that item is defective = P(D)
Using total probability theorem, we get
Hence, the probability that the item defective is 0.0235.
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