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

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b