Mathematics, 02.11.2019 03:31 jerry7792

Schizophrenia affects about 1% of the population. imagine that scientists discover a simple blood test that can tell with 95% accuracy whether a person will develop schizophrenia. that is, 95% of the people who actually will develop schizophrenia will correctly test positive (but 5% will falsely test negative), and 95% of the people who actually will never develop schizophrenia will correctly test negative (but 5% will falsely test positive). you take the test and the results come back positive. what is the approximate probability that you will actually develop schizophrenia?

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Answer from: harkey

Using the Naive Bayes rule ; the probability that a tested person actually develops schizophrenia given that test result comes back positive is 0.161

Naive Bayes rule :

$P(A|B) = \frac{P(B|A) * P(A)}{P(B)}$ P(A|B) = P of A being True given that B is True P(A) = probability of A P(B|A) = P of B bring true given that A is True P(B) = probability of B

Let :

P(A) = Probability of Schizophrenia = 1% = 0.01P(B) = probability of True positive result P(A|B) =? P(B|A) = P of positive result given person has schizophrenia = 95% = 0.95

The probability of obtaining a positive result :

P(B) = [P(B|A) × P(A)] + [P(B|A)' × P(A)']

P(B) = (0.95 × 0.01) + (0.05 × 0.99)

P(B) = 0.059

Hence,

$P(A|B) = \frac{0.95 \times 0.01}{0.059} = \frac{0.0095}{0.059} = 0.161$

Therefore, the probability of schizophrenia given a true positive result is 0.161

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Answer from: reneewilliams20

If you test positive, the approximate probability that you will actually develop schizophrenia is 16.10%.

Step-by-step explanation:

We have these following probabilities:

A 1% probability of having Schizophrenia.

A 99% of not having Schizophrenia.

If a person has Schizophrenia, a 95% probability of testing positive.

If a person does not have Schizophrenia, a 5% probability of testing positive.

What is the approximate probability that you will actually develop schizophrenia?

This can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

$P = \frac{P(B).P(A/B)}{P(A)}$

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

So:

What is the probability of you developing schizophrenia, given that you tested positive?

P(B) is the probability of the person having the disease. So P(B) = 0.01

P(A/B) is the probability of the person being diagnosticated, given that she has the disease. So P(A/B) = 0.95 .

P(A) is the probability of the person being diagnosticated. That is 95% of 1% and 5% of 99%. So

P(A) = 0.01(0.95) + 0.99(0.05) = 0.059

Finally

$P = \frac{P(B).P(A/B)}{P(A)} = \frac{0.01*0.95}{0.059} = 0.1610$

If you test positive, the approximate probability that you will actually develop schizophrenia is 16.10%.

Answer from: Quest

answer: it is d

step-by-step explanation:

Answer from: Quest

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