XYZ, Inc. manufactures the same product in two of their plants, a Northern facility and a Southern facility. Customers who purchase from XYZ, Inc. are encouraged to return their products if they are defective. The probability that a customer returns his/her purchased product given that it was manufactured in the Southern facility is 0.15. The Southern facility produces 40% of the products. It has been recorded that 8% of the customers return their product. What is the probability that a product has been manufactured in the Southern facility if it has been returned to XYZ, Inc.

= 0.75

Step-by-step explanation:

given that;

P ( returned product / southern fac.) = 0.15

probability of being manufactured in Southern facility P(S) = 40% = 0.40

so probability of being manufactured in norther facility P(N) = 0.60

probability of product being returned =P(R) =0.08

therefore P(RnS) = P(S) * P(R|S)

= 0.40 * 0.15

= 0.06

so now the probability that a product has been manufactured in the Southern facility if it has been returned to XYZ

= P(S|R) = P(RnS)/P(R)

= 0.06 /0.08

= 0.75

that is the sum

step-by-step explanation:

there are no other answers without knowing the variables values

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.