Question

Four percent of the welds on an automobile assembly line are defective. The defective welds are found using an X-ray machine. The machine correctly rejects 92% of the defective welds and correctly accepts 99% of all of the good welds.

Required:
a. Make a table or a tree to represent this situation.
b. What is the probability that the X-ray machine will diagnose a weld as being defective in a randomly chosen automobile?
c. If the X-ray machine detects a defective weld, what is the probability that the weld really is defective?

Answer 1

a ) See Annex

b) P₁ = 0,0464 or P₁ = 4,64 %

c) P₄ = 0,92 or P₄ = 92 %

Explanation:

b) P₁ [ X being defective ] = P₂ + P₃

Where P₂ is the probability of X rays machine detects a weld defective and the weld is really defective

And P₃ is the probability of X rays machine detects a weld defective and the weld is not defective

Then

P₂ = 0,04 * 0,92 = 0,0368

P₃ = 0,96 * 0,01 = 0,0096

Then P₁ = 0,0368 + 0,0096

P₁ = 0,0464 or P₁ = 4,64 %

c) P₄ = 0,04 *0,92

P₄ = 0,92 or P₄ = 92 %