Probability

quiz 1

experiment

an activity or procedure that produces distinct, well-defined possibilities

sample space

set of all outcomes

event

particular subset of the sample space (specific)

a set can be defined as…?

a collection of UNIQUE events (no duplicates)

general equation for probability is…?

# of successful / favorable outcomes/ # of total outcomes

probability is always between what two numbers?

0 and 1

under what circumstances does the general formula of probability work?

1. if there are finitely many outcomes

2. if all outcomes are equally likely

Ex: If you have a weighted die, and the probability of rolling a 6 is 50% while the probability of rolling a 1 is 2%, what is the probability of all other equally likely outcomes?

You add the the given probabilities (as decimals), subtract that sum from 1, then divide by the number of equally likely outcomes. (1 - 0.5 - 0.02) / 4 = 0.12 or 12%

disjoint events

events that cannot occur at the same time, no common outcomes

outcomes are represented by what greek letter?

lowercase omega (w)

sample size is represented by what greek letter?

capital omega

What are the four axioms of probability?

1. For any event A, probability is always 0 to 1

2. If omega is the sample size, then P(capital omega) = 1

3. If A and B are disjoint events, then P(A U B) = P(A) + P(B)

4. If A1, A2… is an infinite sequence of pairwise disjoint events (no two sets are common), then the probability is the sum of all events

union means what…?

meaning A OR B, listing all the values while keeping the set unique

intersection means what…?

meaning A AND B, listing common or shared values between the events

Define the compliment of an event (ex: A^c)

meaning any outcomes that are not in event A

What does the probability of monotonicity state?

if A is a subset (c) of B (meaning all outcomes in A are in B) then P(A)<_ P(B)

What are two other properties along with the monotonicity property?

1. if A^C is the complement of A, then P(A) = 1 - P(A^C)

2. for any events A and B, P(A U B) = P(A) + P(B) - P(A intersection B)