Question

Suppose it is known that 1 part in 1000 produced by an aircraft supplier is bad. Each part can be screened for defects using x-rays. If the part is bad, the x-ray test will detect it with probability 0.999. If the part is good, there is a probability of 0.002 that it is erroneously indicated as bad by the x-ray test. For one randomly selected part, the test shows that it is bad. What is the probability that it is really bad (hint: this is a conditional probability)?

Answer 1

Answer:0.333

Step-by-step explanation:

Given

$P\left ( bad aircraft\right )=0.001$

$P\left ( positive|if bad\right )=0.999$

$P\left ( Positive|no bad\right )=0.002$

$P\left ( bad|positive\right )=\frac{P\left ( positive|bad\right )\times P\left ( bad\right )}{P\left ( positive\right )}$

$P\left ( Positive\right )=0.002\times 0.999+0.999\times 0.001=0.002997$

$P\left ( bad|positive\right )=\frac{0.999\times 0.001}{0.002\times 0.999+0.999\times 0.001}$

=0.333