Basics of Probability
What is the word used for a tool that behaves similarly to actually performing a procedure, but saves us a lot of time and effort, as it does all of the time-consuming work for us.
Simulation(s)
Use the Fundamental Counting Rule to determine the following prompt...
Jim has 3 pairs of pants, 5 shirts, and 2 pairs of shoes. How many different ways can Jim dress?
3*5*2 = 30
30 ways
The probability of an event is a fraction or decimal between what two numbers?
0 and 1
An event is this if its probability is very small, such as 0.05 or less
Unlikely
For which does order matter...permutations or combinations?
Permutations
Which approach of probability involves relying on our knowledge of certain circumstances to make an educated guess?
Ex. What is the probability that Mr. Hodges wears bright pink cowboy boots to school tomorrow?
Subjective Probability
What is the value of 8! ?
40320
If a decimal isn't "nice", how many significant digits should the rounding include?
3
Ex. 2/9 = .222
This is any event combining two or more simple events
Compound event
What notation do we use to show that a probability is very small (Ex: 0.0000000123) so it can be known that is extremely close to zero while still being possible?
0+
Which approach of probability requires that the outcomes are equally likely?
Typically denoted as P(A) = number of ways A can occur over number of different simple events
In how many ways can you rank your 3 favorite movies from a random list of 10 different movies?
720 ways
(Permutation with all items different)
Can P(B l A) be the same as P(A l B)
Yes, rarely tho
This event is denoted by placing a bar over the event letter, which consists of all outcomes in which that event does not occur.
Complement
What is the key word that indicates addition of probabilities?
What is the key word that indicates multiplication of probabilities?
Addition: or
Multiplication: and
List the sample space of flipping a coin 3 times.
Ex {bbb, bbg, bgb, ...}
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
How many ways can the letters in "Mississippi" be arranged if they are selected without replacement?
Note: there are some repeated or similar letters.
34,650
(Permutation with some repeated or similar items)
Under what threshold can we treat selections as independent even if they are dependent to avoid extremely tedious or cumbersome calculations?
I'm looking for the number or percent that the sample size must be in comparison to the population size.
0.05 or 5%
Disjoint or Mutually Exclusive
What was the Rule for Inferential Statistics that said "under a given assumption, the probability of a particular observed event is extremely small, we conclude that the assumption is probably not correct"
Rare Event Rule for Inferential Statistics
(Rare Event)
What is the law that states that if a procedure is repeated over and over, the relative frequency will typically be close to approach the actual probability
Law of Large Numbers
How many ways can 3 students be picked from a list of 8 students?
56 ways
(Combination)
FINAL JEOPARDY
"Events A-B-C, it's easy as Probability"
Type of probability that is obtained with the additional information that some other event has already occurred. P(B l A) is an example of this kind of probability.
Conditional probability
When making selections with replacement, are those selections independent or dependent?
Independent