Learning Resources
Lesson
Case Study 1: Toast
This case study obviously deals with experimental probability. There is no way to get the necessary data other than by using an experiment. Because bringing buttered toast into the classroom may not meet with too much favor from your principal, the experiment has been performed for you and the results supplied.
Case Study 2: Birthday
Caution: Question (a) is somewhat deceptive. The temptation is to reason as follows: since there are 365 days in a year, the probability that any given student's birthday falls on a particular day (viz. your birthday) is 
. That is a correct statement. The mistake occurs when we multiply this probability by the number in the class. For example, if there are 10 people in class the probability that "someone" has the same birthday as you is NOT 
. It may be close to it but it is not equal to it. You can see this if you take the extreme case, viz. a class of 365. Using this reasoning, the probability "someone" has the same birthday as you would be 
or 1. It would be guaranteed but quite obviously that is not the case. You have to account for the fact that some of the 365 may have the same birthday. That calculation is difficult even for 2 people as indicated in question (b). Think about the problem but you may not be able to find the solution.
For Question (b) it is easier to calculate the probability of the complement and then subtract from 1 to get the probability of the event. Calculate the probability that the second person's birthday is different than the first. For example, since there are 365 days in the year on which the first birthday can fall, there are 364 "other days" on which the second birthday can fall and be different. Thus the probability the second birthday is different is 
. Similarly, the third birthday could fall on any of 363 days and be different. and its probability is 
. Depending on the number of students, these probabilities continue to decrease and the probability of all events occurring can be found using the multiplication principle.
This is the probability all the birthdays are different, call it P(X). The probability that at least two are the same is therefore 1 - P(X).
Activity
Depending on the time you have, complete either Case Study 1 or 2 on page 351 in your text. If you have the time and interest complete both of them. Case Study 2 is very challenging and you may require some help from your online teacher to complete it.
Test Yourself
There are no test items for the Case Studies.