Program Crashes

A company has bought three software packages for their operations. They are Abacus, Biscuit and Circuit. On average, Abacus crashes 1 in 200 times, Biscuit 1 in 10 times, and Circuit 1 in 50. Of the ten employees, two were assigned Abacus, five got Biscuit, and three received Circuit. If Sophia’s trial crashed on the first trial, what is the probability that she got Abacus?

Use Bayes’ equation to get the answer:

\\ P(A|CR) = \frac{P(CR|A) * P(A)}{P(CR|A) * P(A) + P(CR|B) * P(B) + P(CR|C) * P(C)} \\ \\ = \frac{(1/200) * (0.2)}{(1/200) * (0.2) + (1/10) * (0.5) + (1/50) * (0.3)} = 0.01754

Reference

An Introduction to Probability and Interactive Logic by Ian Hacking