Conditional Probability and Independence

Question 1

What is conditional probability?

Answer 1

Conditional probability occurs when the probability of an event changes given that another event has occurred. Review equation for conditional probability.

Question 2

What’s the deal with conditioning and the multiplication rule?

Answer 2

Conditioning should lead to easier probabilities, if not it will just make things too difficult or ambiguous. The multiplication rule is derived from the conditional probability equation and is helpful in determining intersections of events.

Question 3

What is the law of total probability?

Answer 3

Thanks to the law of total probability we can compute the probability of an arbitrary event through conditioning on several disjoint events that make up the whole sample space. Review the mathematical definition of the law.

Question 4

What is Bayes’ Rule?

Answer 4

Bayes’ Rule is a rule derived from the law of total probability where you can compute then conditional probability of one of the disjoint events that make up the whole sample space given that an arbitrary event has occurred. Review the mathematical definition.

Question 5

What is the concept of independence?

Answer 5

Two events A and B are independent if and only if the probability of A given B is the probability of A. Because A remains unaffected whether B occurs or not. Review the three equations that prove independence.

Question 6

What’s the deal with the independence of more than two events?

Answer 6

The probability of the intersection of the events must be equal to the product of the individual probabilities of the evens. Check book for a clear mathematical definition.