Answer:
Step-by-step explanation:
1. You have the following information given in the problem:
- The distance to the nearest exit door is no more than 150 feet.
- represents the distance to the nearest exit door, in feet.
2. Therefore, keeping the information above on mind, you know that the distance to the nearest exit door () must be less than or equal to 150 feet, then, you can express this as following:
Answer:
(a) The probability tree is shown below.
(b) The probability that a person who does not use heroin in this population tests positive is 0.10.
(c) The probability that a randomly chosen person from this population is a heroin user and tests positive is 0.0279.
(d) The probability that a randomly chosen person from this population tests positive is 0.1249.
(e) The probability that a person is heroin user given that he/she was tested positive is 0.2234.
Step-by-step explanation:
Denote the events as follows:
<em>X</em> = a person is a heroin user
<em>Y</em> = the test is correct.
Given:
P (X) = 0.03
P (Y|X) = 0.93
P (Y|X') = 0.99
(a)
The probability tree is shown below.
(b)
Compute the probability that a person who does not use heroin in this population tests positive as follows:
The event is denoted as (Y' | X').
Consider the tree diagram.
The value of P (Y' | X') is 0.10.
Thus, the probability that a person who does not use heroin in this population tests positive is 0.10.
(c)
Compute the probability that a randomly chosen person from this population is a heroin user and tests positive as follows:
Thus, the probability that a randomly chosen person from this population is a heroin user and tests positive is 0.0279.
(d)
Compute the probability that a randomly chosen person from this population tests positive as follows:
P (Positive) = P (Y|X)P(X) + P (Y'|X')P(X')
Thus, the probability that a randomly chosen person from this population tests positive is 0.1249.
(e)
Compute the probability that a person is heroin user given that he/she was tested positive as follows:
Thus, the probability that a person is heroin user given that he/she was tested positive is 0.2234.