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?

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 :

Let :

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,

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

Learn more :link

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

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

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

Finally

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

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions