Common Mistakes on HW 11
- (5.3) Problem 36: Be careful about not burying "+1" in induction proofs. The grader remarked that this was often forgotten about halfway through the induction step (i.e. 'm+1' was mistaken as 'm' somewhere, and then the proof did not work).
(6.1) Problem 10: Don't assume that the selection is followed by a replacement (it isn't, here--"all five bulbs are good" means just that, i.e. you're not putting the bulb back in the box after checking it). Also, make sure that your event E is actually a subset of your sample space. E.g. if the numerator is a number of ordered arrangements / choices, then same should apply to the denominator. (Good practice question to get this clear: How does this work out in the birthday problem?)
(6.2) Problem 6: Don't forget the "\cap" part of P(A \cup B) = P(A) + P(B) – P(A \cap B). Also, make sure to not confuse \cup and \cap.
- (6.3) Problem 12: Review the solution--there seems to have been a lot of confusion here.