Chapter 5: Probability Flashcards
Define Probability
long run relative frequency
number between 0 and 1
no negative numbers
no square roots
Define Law of Large Numbers
more trials of a random process brings you closer to its probability
Interpretation of Probability [P(A)]
After many many __context__, the proportion of time that __context A__ will occur is about __P(A)__.
ex. P(heads)=0.5; After many many __coin flips__, the proportion of times that __heads__ will occur is about __0.5__.
How would you Simulate?
- % chance of __success context__
- # of trials
- Goal
Description of the usage of random digit table to carry out the simulation
- assign # [let 0-3 represent __X__, 4-9 represent __Y__, ignore #-#]
- Ignore repeated numbers
- read random digit table from left to right by # digits each time, stop when # of trials is completed.
- To get the probability of __success context__, analyze data if __goals in 1 group of digits read__ that are not the same numbers and within interval of __assigned #s__.
- calculate
– or use RandInt{lowest #, highest #, how many you want}
Define Disjoint: Addition Rule
P(AUB) = P(A) + P(B)
Disjoint = mutually exclusive = no outcomes in common
Define Complement Rule
P(A^c) = 1-P(A)
A^c, A bar, not A = all same notation
Define Conditional Probability
P(A|B) = P(A and B) / P(B)
Probability of one event happening given another event happened first
Define Independence
if…
- P(A)*P(B) = P(A and B)
- P(A) = P(A|B) = P(A|B^c)
- P(B) = P(B|A) = P(B|A^c)
then… A and B are independent
Events are independent if the occurrence of one event doesn’t change the probability of the other event.
Define Mutually Exclusive
No outcomes in common
Difference between Mutually Exclusive and Independent
- They are not relatable
- mutually exclusive and independent cannot happen at the same time
Define Multiplication Rule
P(A and B) = P(A)P(B|A) = P(B)P(A|B)
The probability that events A and B both occur can be found using the general multiplication rule.
Define Multiplication Rule for Independent Events
P(A and B) = P(A)*P(B)
The probability that events A and B both occur and A and B are independent events.
Interpretation of Conditional Probability [P(A|B)]
Given __context B__, there is a __P(A|B)__ probability of __context A__.
ex. P(red car|pulled over) = 0.48; Given that __a care is pulled over__, there is a __0.48__ probability of __the car being red__.
