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Answer:
(1) The probability of a successful product given the product is favorable is 0.7778.
(2) The probability of a successful product given the product is unfavorable is 0.2391.
(3) The probability of a unsuccessful product given the product is favorable is 0.2222.
(4) The probability of a unsuccessful product given the product is favorable is 0.7609.
Step-by-step explanation:
Denote the events as follows:
<em>S</em> = a product is successful.
<em>F</em> = a product is favorable.
The information provided is:
The law of total probability states that:
Use the law of total probability to compute the probability of a favorable product as follows:
The probability of a favorable product is 0.54.
The conditional probability of an event <em>A</em> given that another event <em>B</em> has already occurred is:
(1)
Compute the value of P (S|F) as follows:
Thus, the probability of a successful product given the product is favorable is 0.7778.
(2)
Compute the value of as follows:
Thus, the probability of a successful product given the product is unfavorable is 0.2391.
(3)
Compute the value of as follows:
Thus, the probability of a unsuccessful product given the product is favorable is 0.2222.
(4)
Compute the value of as follows:
Thus, the probability of a unsuccessful product given the product is favorable is 0.7609.