Notes and Questions on Chapters 13,14,15

The Sample Space, denoted S, of an experiment is a listing of all possible outcomes.  The sample space of rolling a die once has 6 elements, that is {1,2,3,4,5,6}  The sample space of picking a card from a standard deck has 52 elements since there are 52 cards in a standard deck.  The sample space of rolling a pair of dice once has 36 elements, since each die has 6 faces.

 The probability of a particular outcome or an event, denoted P(E), is the likelihood of the event.  P(E)=Number of ways of getting E divided by Number of all possible outcomes of the experiment  The probabilities of individual outcomes in the sample space S add up to 100%!

 Probability of an event E not happening is therefore  P(not E) = 100% - P(E)  P(at least one) = 100% - P(none)  Remember, 100% = 1. You can use either one, but don’t make the mistake such as 100%- 0.4=99.6%; the correct answer should be 0.6.

 Probability of an event A or an event B happening is given by  P(A or B) = P(A) + P(B) – P(A and B)  Here “A or B” means at least one of A or B happens; “A and B” means both A and B happen.

 On the other hand, if there are a number of mutually disjoint (i.e, no two to happen simultaneously) outcomes to an event E, then the probability of E is given by  P(E) = P(Outcome1) + P(Outcome2) + …  Example: Finding the probability of making an A, a B, or a C in a math class.  Example: Finding the probability of rolling a 3 or 4 on a single roll of the die.

 If there are a number of steps to the occurrence of an event E, then the probability of the event E is given by  P(E) = P(Step1) * P(Step 2) * P(Step 3) *…  Example: Finding the probability that you roll a 6 first, then a 2, and then a 3 on three rolls of a die.

 Two events A and B are said to be independent if whether A happens or not has no say in the subsequent likelihood of B and vice versa.  If P(A, given B)=P(A) then A and B are independent;  Or, if P(A and B) = P(A)*P(B), then A and B are independent.