easy Probability

Performance?

A release-checked easy problem for training Bayes' Theorem, Conditional Probability.

Question

A student takes an exam. There is a probability $0 < p < 1$ that they show up on time. If they show up on time, there is a probability $0 < s_1 < 1$ of them getting an A on the exam. If they show up late, there is a probability $0 < s_2 < 1$ of them getting an A on the exam. Given that the student got an A on the exam, find the probability they showed up on-time when $p = 0.8, s_1 = 0.5,$ and $s_2 = 0.1$.

Practice focus

This Probability problem is tagged Bayes' Theorem, Conditional Probability. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.