Acertain virus infects one in every 150 people. a test used to detect the virus in a person is positive 90% of the time when the person has the virus and 5% of the time when the person does not have the virus. (this 5% result is called a false positive.) let a be the event "the person is infected" and b be the event "the person tests positive."(a) using bayes’ theorem, when a person tests positive, determine the probability that the person is infected. (b) using bayes’ theorem, when a person tests negative, determine the probability that the person is not infected.

a) P(A|B)=0.108

b) =0.999

Step-by-step explanation:

Given the events:

A: the person is infected

B: the person tests positive

: the person is not infected

: the person tests negative

a) If we check the attached picture, we can see that:

P(B|A)=

Bayes' Theorem:

P(B)= P(B∩A) + P(B∩)

P(B)= P(B|A)×P(A) + P(B|)×P()

P(B)=

We have to find the probability that the person is infected given that a person tests positive.

P(A|B)==

b) We have to find the probability that the person is not infected given that a person tests negative:

=

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step-by-step explanation:

c.

step-by-step explanation:

substitution for (0,1)

y=x^2+4x+1

1=0^2+4(x)0+1

1=0+4(x)0+1

1=4(x)0+1

1=0+1

1=1

substitution for (-3,-2)

y=x+1

-2=-3+1

-2=-2