11/13 Basic probability

Probability in our context has to do with the outcomes of repeatable experiments

Need an Experiment Set X of outcomes (outcome space) from the experiment: They

should be disjoint (mutually exclusive) and exhaustive (include all possible outcomes)

Events are sets of outcomes (subsets of the outcome space). We want to be able to assign a probability that an event E will occur when the experiment is repeated.

Example: A pair of dice are rolled.

What is the outcome space?

Let E be the event ‘a 7 is rolled’

Let F be the event ‘an 11 is rolled’

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Basic properities of a probability function.

Outcomes: S = {x1, x2, x3, …E, F events

1. P(E) >= 0 for any event E.

2. P(S) = 1

3. If E and F are mutually exclusive, then

Consequences:

4.

5.

Uniform probability function: Each outcome has the same probability. Define the probability of an event ETo be P(E) = n(E)/n(X) where X is the outcome space.

The 3 rules of probability hold ( and so all of the consequences hold)

Sampling to discover probabilities

Common #14 An experiment consists of studying the hair color of all members of families with one child.

Sampling to discover probabilities

Common #6 By sampling, a cell-phone provider discovers That 2% of calls fail to reach the network, another 5% are dropped by the network and an additional 2% fail to reachthe callee. What is the probability that random cell call willfail to connect?

Calculating probabilities in games:

Lottery. What is the probability of winning Powerball?

Calculating probabilities in games:

Poker: What is the probability of getting a flush in a random 5 card hand?

What is the probability of getting at least a pair in a random5 card hand?