A certain manufactured item is visually inspected by two different inspectors. When a defective item comes through the line, the

Question

1 month ago

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A certain manufactured item is visually inspected by two different inspectors. When a defective item comes through the line, the

probability that the first inspector misses it is 0.1. Of those that get past the first inspector, the second inspector will "miss" 5 out of 10. What fraction of defective items get by both inspectors?

Mathematics

1 answer:

tester [12.3K] · Answer 1 · 2026-04-02T10:21:33+03:00

The proportion of defective items bypassing both inspectors is $\frac{5}{100}$ = $\frac{1}{20}$

Step-by-step explanation:

Step 1; Let's say the likelihood of the first inspector not spotting a defective item is P(A), while P(B) is the chance that the second inspector overlooks those that have passed the first inspector. Step 2; Given that P(A) equals 0.1, we convert it into a fraction to ensure our final probability is a fraction as well.P(A) = 0.1 =

.

Since the second inspector fails to detect 5 out of 10 that go past the first inspector, thus P(B) =

.

Step 3; To determine the probability of both inspectors missing a defective item, we multiply the two probabilities together. $\frac{1}{10}$ P(A and B happening)

= P(A) × P(B) =

× = = $\frac{5}{10}$ =

0.05%

. Thus, the chance of both inspectors missing a defective part is a mere 0.05% chance.