Say in Silicon Valley, 35% of engineers program in Java and 28% of the engineers who program in Java also program in C++. Furthermore, 40% of engineers program in C++.
a. What is the probability that a randomly selected engineer programs in Java and C++?
b. What is the conditional probability that a randomly selected engineer programs in Java given that they program in C++?
For A, I got 35 * 0.28 = 9.8.
B is what I'm confused by. How do I calculate a conditional probability that a randomly selected engineer programs in Java given that they program in C++? Is this using Bayesian Theorem?
the solution is pretty much the same as
Is there a formula I can use to solve this probability problem?
it involves Bayes theorem
https://en.wikipedia.org/wiki/Bayes%27_theorem
https://youtu.be/HZGCoVF3YvM from 3Blue1Brown