Q2

In this question, you'll work on a very common application of Bayes' Theorem.

Marie is getting married tomorrow at an outdoor ceremony in the desert. In recent years, it has rained only 3 days each year. Unfortunately, the weatherman has predicted rain for tomorrow. When it actually rains, the weatherman correctly forecasts rain 95% of the time. When it doesn't rain, he incorrectly forecasts rain 5% of the time. What is the probability that it will rain on the day of Marie's wedding?

To answer this question, you'll need to use Bayes' Theorem. Recall:

We'll call event A "it rains", and event B "the weatherman forecasts rain." What is $P(A | B)$, or the probability of rain given that the weatherman has predicted rain?

Hint: You can rewrite $P(B)$ using the chain rule of probability to be: $P(B | A ) * P(A) + P(B | !A) * P(!A)$, where ! means "negation", or the opposite.

In addition to the final answer, please include your thought process. And please don't consult Google.