The Bayes' Theorem is used to calculate conditional probabilities, that is, the probability of occurrence of an event given another event has already occurred.
The formula is:
[tex]P(A|B)=\frac{P(B|A)\times P(A)}{P(B)}[/tex]Let's call:
Event A = Eat pizza for dinner
Event B = Go to bed early
We are given the following probabilities:
P(A) = 65% = 0.65
P(B) = 58% = 0.58
P(B|A) = 82% = 0.82
Substituting:
[tex]P(A|B)=\frac{0.82\times0.65}{0.58}=0.9190[/tex]Answer: 91.90%
