<img src="https://tex.z-dn.net/?f=%5Cfrac%7B12%7D%7B20%7D%3D" id="TexFormula1" title="\frac{12}{20}=" alt="\frac{12}{20}=" align

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lions [1.4K]

1 year ago

="absmiddle" class="latex-formula"> ____% = ____ hundredths

Mathematics

1 answer:

Alecsey [184]1 year ago

5 0

The equivalent numbers of 12/20 are 60% and 0.60

<h3>How to convert the fraction?</h3>

The fraction expression is given as:

12/20

Multiply the fraction expression by 100%

So, the expression becomes

12/20 * 100%

Evaluate the product

60%

Express as fraction, again

60/100

Evaluate the quotient

0.60

Hence, the equivalent numbers of 12/20 are 60% and 0.60

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In a large population, 3% of the people are heroin users. A new drug test correctly identifies users 93% of the time and correct

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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:

$P(X\cap Y)=P(Y|X)P(X)=0.93\times0.03=0.0279$

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')

$=(0.93\times0.03)+(0.10\times0.97)\\=0.1249$

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:

$P(X|positive)=\frac{P(Y|X)P(X)}{P(positive)} =\frac{0.93\times0.03}{0.1249}= 0.2234$

Thus, the probability that a person is heroin user given that he/she was tested positive is 0.2234.

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