Answer:
Probability of a train on line A arriving on time: 80%
Probability of any train arriving on time: 96%
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%