Title: 1113 Basic probability
111/13 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.
2Example 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
3- 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
- If E and F are mutually exclusive, then
- Consequences
- 4.
- 5.
4Uniform probability function Each outcome has
the same probability. Define the probability
of an event E To 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)
5Sampling to discover probabilities Common 14
An experiment consists of studying the hair
color of all members of families with one child.
6Sampling 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 reach the callee. What is
the probability that random cell call will fail
to connect?
7Calculating probabilities in games Lottery.
What is the probability of winning Powerball?
8Calculating 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 random 5 card
hand?