To determine if being subjected to an additional search is independent of carrying a laptop computer, we can calculate the conditional probability of being searched given that a passenger carries a laptop and compare it to the probability of being searched overall.
The probability of being searched overall is the number of passengers searched divided by the total number of passengers, which is 175/420 = 41.7%.
The probability of being searched given that a passenger carries a laptop is the number of passengers searched who carry a laptop divided by the total number of passengers who carry a laptop, which is 30/72 = 41.7%.
Since the probability of being searched is the same regardless of whether or not a passenger carries a laptop, it appears that being subjected to an additional search is independent of carrying a laptop.
For part B, the probability of selecting a passenger who carries a laptop and is not searched is 42/420 = 10%.
For part C, the probability of selecting a passenger who is not searched or carries a laptop is (203 + 145)/420 = 53.8%.
For part D, the probability of a passenger carrying a laptop given that they are searched is 30/175 = 17.1%.