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?

Answer 1

There are 70/2 = 35 suitcases with the substance. The probability of not detecting the substance is 1.00 - 0.68 = 0.32. Therefore the expected number of times the substance is not detected is:
$35\times0.32 = 11\ times\ (approximately)$