Final answer:
The probability of a polygraph test correctly detecting a lie given a 72% success rate is 72%. If the same rate applies to detecting the truth, that probability is also 72%. These results suggest a 28% chance of false readings.
Step-by-step explanation:
If a polygraph test has an approximately 72% success rate in detecting lies, the probability of it correctly detecting a lie can be expressed as 0.72 or 72%. This probability can be directly calculated using the given success rate.
b) The calculation for the probability of detecting the truth would require additional information about the test's overall accuracy, including its true positive and false positive rates. However, if we assume that the polygraph has the same accuracy rate for detecting the truth as it does for lies, then the probability would also be 0.72 or 72%.
c) Interpreting the results of these calculations suggests that the polygraph is correct about 72% of the time when it indicates someone is lying or telling the truth. This implies that in about 28% of cases, the polygraph might give a false reading, either indicating a lie when the truth is being told or failing to detect a lie.