Mathematics, 19.02.2020 23:25 wilneishawatkins

A study of the US clinical population found that 24.1% are diagnosed with a mental disorder, 14.9% are diagnosed with an alcohol-related disorder, and 5% are diagnosed with both disorders.

(a) What is the probability that someone from the clinical population is diagnosed with a mental disorder, knowing that the person is diagnosed with an alcohol-related disorder? Please use 3 decimal places.

(b) What is the probability that someone from the clinical population is diagnosed with an alcohol-related disorder, knowing that the person is diagnosed with a mental disorder? Please use 3 decimal places.

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Answer from: Hailey1313131313

a) 0.336

b) 0.207

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

We solve this problem building the Venn's diagram of these probabilities.

I am going to say that:

A is the probability that a person from the clinical population is diagnosed with mental disorder.

B is the probability that a person from the clinical population is diagnosed with alcohol related disorder.

We have that:

$A = a + (A \cap B)$

In which a is the probability that a person is diagnosed with mental disorder but not alcohol related disorder and $A \cap B$ is the probability that a person is diagnosed with both of these disorders.

By the same logic, we have that:

$B = b + (A \cap B)$

We find the values of a,b and the intersection, starting from the intersection.

5% are diagnosed with both disorders.

This means that $A \cap B = 0.05$

14.9% are diagnosed with an alcohol-related disorder

This means that B = 0.149

$B = b + (A \cap B)$

0.149 = b + 0.05

b = 0.099

24.1% are diagnosed with a mental disorder

This means that A = 0.241

$A = a + (A \cap B)$

0.241 = a + 0.05

a = 0.203

(a) What is the probability that someone from the clinical population is diagnosed with a mental disorder, knowing that the person is diagnosed with an alcohol-related disorder?

Desired outcomes:

Mental and alcohol-related disorders, which $A \cap B$ . So D = 0.05

Total outcomes:

Alcohol-related disorder, which is B. So T = 0.149

Probability:

$P = \frac{0.05}{0.149} = 0.336$

(b) What is the probability that someone from the clinical population is diagnosed with an alcohol-related disorder, knowing that the person is diagnosed with a mental disorder?

Desired outcomes:

Mental and alcohol-related disorders, which $A \cap B$ . So D = 0.05

Total outcomes:

Mental disorder, which is B. So T = 0.241

Probability:

$P = \frac{0.05}{0.241} = 0.207$

Answer from: Quest

stew reads at the fastest rate of 265 words per minute.

step-by-step explanation:

it's a given that felicia reads at 260 word per minute and on connie's graph we can see that she reads 200 words per minute. since stew's table tells us that he read 795 in 3 minutes, we can divide 795 by 3 to find out how many words he reads per minute.

795/3 = 265

stew reads 265 words per minute - he reads at the fastest rate since felecia reads at 260 words per minute and connie reads at 200 words per minute.

stew (265) > felecia (260) > connie (200)

Need 45 ! compare the rates at which each of the three students read: which student read at a fa

Answer from: Quest

step-by-step explanation:

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