A witness identified a suspect as having blond hair. However, when tested under lighting conditions similar to those on the night of the incident, it was concluded that the probability of correctly identifying blond hair was 0.90 and the probability of being incorrect about non-blond hair was 0.2. Suppose that 0.4 is the proportion of persons with blond hair that live in the area. Let two events A and B be defined as A = [ Identified as blond and B = [ Person is blond] 1. Fill in the four probabilities, and the marginal totals, in the two-way table. using... (A, B, Not A, Not B) 2. Given that this person was identified as blond, find the probability of being blond 3. Make a Venn diagram to display the relations among these two events.

To get the table we have to find the following probabilities

p(A), p(B), p(not A), p(not B)

A = suspect has blond hair

B = suspect is blond

p(B) = 0.4

probability of identifying correctly = AIB = 0.90

prob of wrongful identification =  AlB' = 0.2

Probability of A = p(AIB) *p(B) + p(AIB')*p(B')

= 0.9 * 0.4 + 0.2 *(1-0.4)

= 0.48

p( not A) = 1-0.48 = 0.52

p(not b) = 1-0.40 = 0.6

the table  has been added as an attachment

2. probability of being blond = 0.9 * 0.4 / 0.48 = 0.75

3. p(A∩B) =  0 .90 * 0.4 = 0.36

the venn diagrams an attachment also

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c

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.