A train station employee collects data on 160 incoming trains to the station. He notices that 18 of the 90 incoming trains on line A arrive late, and 14 of the 70 incoming trains on line B arrive late.

What is the probability that a train on line A arrives on time? What is the probability that any train arrives on time?

Probability of a train on line A arriving on time: 80%

Probability of any train arriving on time: 96%

Step-by-step explanation:

If 18 of the 90 incoming trains on line A arrive late, we have that 90 - 18 = 72 trains of the 90 arrive on time, so the probability of a train on line A arriving on time is:

P (A) = 72/90 = 0.8 = 80%

on line B, we have that 70 - 14 = 56 trains of the 70 arrived in time, so the probability of a train from line B arriving on time is:

P (B) = 56/70 = 0.8 = 80%

To find the probability of any train arriving on time, we can use this formula:

P (A or B) = P (A) + P (B) - P (A and B)

P (A or B) = 0.8 + 0.8 - 0.8*0.8

P (A or B) = 1.6 - 0.64 = 0.96 = 96%