A theater is selling movie tickets. The first night, 19 Senior tickets and 57 Adult tickets were sold. The second night, 20 Seni
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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.
Answer:
The graph is shown below.
The time to make the taste to half is <u>4.265 s.</u>
Step-by-step explanation:
Given:
Initial value of the taste is,
Therefore, the quality of taste over time 't' is given as:
Now, when the taste reduces to half,
Therefore,
Taking natural log on both the sides, we get:
Therefore, the time to make the taste to half is <u>4.265 s.</u>
