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

Answer:

a ) See Annex

b) P₁  =  0,0464       or    P₁  =  4,64 %

c) P₄  = 0,92   or   P₄  = 92 %

Step-by-step 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 %