Only 1% of 40-year-old women who participate in a routine mammography test have breast cancer. 80% of women who have breast cancer will test positive, but 9.6% of women who don’t have breast cancer will also get positive tests. suppose we know that a woman of this age tested positive in a routine screening. what is the probability that she actually has breast cancer?

Probability that the woman has really breast cancer if the test result is positive = 0.077

Step-by-step explanation:

Given,

    Probability that the woman has breast cancer, P(B) = 0.01

=> Probability that the woman has breast cancer, P(B')=1-0.01= 0.99

    Probability that test will be positive if woman has breast cancer,P(T/B) = 0.8

=>Probability that test will be negative if woman has breast cancer,P(T'/B) =1-0.8= 0.2

 Probability that test will be positive if woman hasn't breast      cancer,P(T/B')=0.096

=>Probability that test will be negative if woman hasn't breast cancer,P(T'/B')=1-0.096=0.904

So, the probability that the test will show positive result either the disease is present or not,

P{T} = P(T/B).P(B)+P(T/B').P(B')

       = 0.8 x 0.01 + 0.096 x 0.99

       = 0.10304

Now, the probability that the woman has really breast cancer if the test result is positive,

                  = 0.077

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.