Suppose that 95% of the fasteners pass the initial inspection. Of those that fail the initial inspection, 20% are defective. Of the fasteners sent to the recrimping operation, 40% cannot be corrected ad are scrapped; the are corrected by the recrimping and then pass inspection.

A. What proportion of the fasteners that fail the initial inspection pass the second inspection (after the recrimping operation) ?

B. What proportion of fasteners pass inspection?

C. Given that a fastener passes inspection, what is the probability that it passed the initial inspection and did not have to go through the recrimping operation?

Answer

Step-by-step explanation:

Let x be the fasteners

95% of x passed, and 5% of x failed

20% of the 5% which failed are defective, remaining the 80% of the failed 5%.

Now 40% of this 80% of the 5% which failed are scrapped, meaning only the remaining 60% passed second inspection.

Thus

a). The proportion;

60% of 80% of 5% of x

mathematically

= 60/100 * 80/100 * 5/100

= 0.024 or 2.4%

b) initially 95% passed and later on 2.4% pass again. Therefore total that passed = 95%+2.4%=97.4%

c) probability that it passed on first inspection is 95/100

Percentage that went through recrimping = 80% of 5% = 80/100 * 5/100 = 1/25 or 0.04 or 4%

Thus probability of passing and not going through recrimping

= 1 - (1/25) = 0.96 or 96%