Question
When a sample space is partitioned into mutually exclusive events Bi, how do you find P(A)?
Tap to flip
Answer
Apply total probability: P(A)=∑P(A∣Bi)P(Bi).
Tap to flip back
Question
How do you compute the probability of either of two events occurring when they may overlap?
Tap to flip
Answer
Use P(A or B)=P(A)+P(B)−P(A and B).
Tap to flip back
Question
How does conditional expected value incorporate new information?
Tap to flip
Answer
It reweights outcomes using conditional probabilities: E(X∣info)=∑P(xi∣info)xi.
Tap to flip back
Question
Why is Bayes' formula important in probability problems?
Tap to flip
Answer
It updates a prior probability using new information.
Tap to flip back