Write an equation of the line passing through point P(4, -6) that is perpindicular to the line y= -3.
1 answer:
You might be interested in
a.
In order to find the common ratio, we just need to divide a term by the term that comes before it.
So using the terms 20 and -5, we have:
b.
The recursive rule can be found with the formula:
Where an is the nth term and q is the ratio. So we have:
c.
The explicit rule can be written as:
Where an is the nth term, a1 is the first term and q is the ratio. So:
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.