3.1-3.2
What are the different types of probabilities?
Theoretical, experimental, and subjective
What is an Independent event?
Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event.
Ex: If we roll a die twice, the outcome of the first roll and second roll have no effect on each other, therefore it's independent.
What does it mean when two events are mutually exclusive?
Mutually Exclusive means that two or more events that cannot happen simultaneously.
If "and" were in a word problem what would that be telling you to do?
Multiply.
The access code for a vault security system consists of 4 digits. The first digit cannot be zero and the last digit must be odd.
How many different codes are available?
4,500 codes
What will you be calculating?
The probability of different things happening
What is a Dependent event?
Dependent events are those which depend upon what happened before. These events are affected by the outcomes that had already occurred previously.
Ex: Not paying your power bill on time and having your power cut off or being the first person to enter a movie theater and finding a good seat.
I this problem mutually exclusive?
Ex: When a coin is tossed
Answer: Not Mutually Exclusive
Permutations
An ordered arrangement in which r objectrs are chosen from n different objects and repetition is not allowed.
Your roommate wants you to help her pick out a car. She has 4 options for color, 3 options for trim and 2 options for seats. How many different ways could she make a car?
24 ways
What is an experimental probability?
The probability of an event actually happening
Ex: A test occurs to determine what the probability of the event is, using a specific formula to compare the number of times the event took place and the total number of times the experiment was executed.
How do you calculate the probability of events happening in a sequence?
The probability of two or more independent events occurring in sequence can be found by computing the probability of each event separately and then multiplying the results together.
What are conditional probabilities?
p(A|B) is the probability of event A occurring, given that event B occurs.
Ex: Given that you drew a red card, what's the probability that it's a four (p(four|red))=2/26=1/13. So out of the 26 red cards (given a red card), there are two fours so 2/26=1/13.
What is the equation for Permutation?
nPr
Event A: Randomly selecting a black queen from a deck of cards. Event B: Randomly selecting a red 4 from a deck of cards. Are these events mutually exclusive?
Yes, it is mutually exclusive.
What is a theoretical probability?
Theoretical probability describes how likely an event is to occur.
Ex: We know that a coin is equally likely to land heads or tails, so the theoretical probability of getting heads is 1/2.
Probability
A number between 0 and 1 that reflects the likelihood of some event (outcome)
How to calculate probabilities using a chart or a diagram?
If you use a histogram or bar chart, by examining the various outcomes along the x-axis and the expected probability of occurrence on the y-axis, you create a very concise and easily read summary of the distribution of outcome probabilities.
Combination
A collection, without regard to order, of n different objects without repetition.
An organization has 55 members. How many different ways can the offices of president, vice-president, secretary and treasurer be filled?
8,185,320 different ways
What is a subjective probability?
Subjective probability is a type of probability derived from an individual's personal judgment or own experience about whether a specific outcome is likely to occur
Ex: If you were to ask several people to estimate the chances that it will be sunny tomorrow, one person might say it's 50%, the next might say 80%, and the next only 25%. These percentages are examples of subjective probability
Sample Size
The collection of all possible outcomes of a probability experiment. (to outline a large sample space often times a tree diagram is used).
What is the fundamental counting principle?
The fundamental counting principle is a rule used to count the total number of possible outcomes in a situation
Ex: If the first event can occur 3 ways, the second event can occur 4 ways, and the third event can occur 5 ways, then you can find out the number of unique combinations by multiplying: 3 * 4 * 5 = 60 unique combinations.
What is the equation for a Combination?
nCr
You have a drawer with 3 pink marbles and 8 green marbles. You pick two gumballs, without putting the first one back.
What is the probability that you pick a green marble and then a pink marble
21.8%