Formula 1 engines

Suppose that two manufacturers, A and B, supply the engines for Formula 1 racing cars, with the following characteristics:

99% of the engines from factory A last more than 5,000 km.
Factory B manufactures engines that last more than 5,000 km with 95% probability.
70% of the engines are from manufacturer A, and the rest are produced by manufacturer B.

What is the chance that an engine will last more than 5,000 km?

100 XP

Calculate the following probabilities: P_A, P_B, P_last5000_g_A, and P_last5000_g_B.
Use the total probability law to answer the exercise question and store the result into P_last_5000.