Question

A company is testing a new device to detect certain substances inside suitcases. Currently, the device is accurate 68% of the time for suitcases that have these substances. In a test where half of the 70 test suitcases carry these substances, about how many times will the test identify a suitcase with the substance as not having it?



11


16


22


48

Answer 1

is my answer 22?

Answer 2

@ganeshie8

Answer 3

I think you might not have read the question carefully enough.

68% of the time, if the detector looks at a suitcase which does have those substances, it will say "substance found" — and 100%-68%=32% of the time when it looks at such a suitcase it will say "substance NOT found"

Half of 70 suitcases contain the substance, so there are 35 suitcases with the substance. 68% of those suitcases will be reported as containing the substance, but the problem asks
"about how many times will the test identify a suitcase with the substance as NOT having it?" (emphasis mine)

68% of 35 is approximately 22 (well, 24), but that's the number of suitcases correctly identified as having the substance. How many of those 35 suitcases will be wrongly identified as not having the substance?

It would be interesting to know if this detector ever gives false positive readings (says the substance is detected, even though it is not present). Nothing is said here about the error rate in that case, but it is an important thing to know in real life!

Answer 4

i dont get it

Answer 5

What don't you get?