Zhaoxin needs to successfully complete a coding project thatinvolves complex natural language processing algorithms. Zhaoxinmust choose between three different Application ProgrammingInterfaces (API), but is unsure which API is best for the project.Being a Statistician, he decides to collect data, then use randomchance to make the final decision. He assigns a probability of 0.45for PyTorch, 0.25 for Keras, and the rest to TensorFlow. Each APIaffects Zhaoxin chances of completing the project on time. Zhaoxinwill complete the project on-time with a 75% chance if he selectsPyTorch, a 55% chance if he selects Keras, and only a 35% chance ifhe selects TensorFlow.
a) Draw a well-labeled tree diagram to illustrate the aboveinformation.
b) What is the probability that Zhaoxin is late and used theTensorFlow API?
c) What is the probability that Zhaoxin is on-time?
d) If Zhaoxin selects Keras as the API, what is the probabilitythat he is on time with the project?
e) If Zhaoxin is late with the project, what is the probabilitythat he selected PyTorch as the API?
f) Is choice of API and project completion independent? Supportyour answer mathematically.
