Probability Flashcards
Familiarise with calculations and concepts
What is logical probability?
Defined by construction of question e.g. how often does a coin toss show heads –> only two possible results in a coin toss
What is empirical probability?
Estimated from previous experience
What is the frequentist definition of probability?
Define an experiment and outcome of interest –> experiment performed N times –> how many times did outcome occur
Probability of outcome (X) = X/N as N continues to infinity
What are three of the main rules of probability?
1) Probability can never be <0 or >1
2) Probability of all possible outcomes sums to 1
3) Probability that an event DOES NOT occur = 1-P
What does a probability of 0 mean?
Improbable but not impossible
What are “odds”?
Probability of an event occurring, divided by probability it won’t occur
e.g. the probability of something occurring is 1/5
The odds for this = (1/5)/(4/5) = 0.2/0.8 = 1:4
To convert the other way, from odds to probability, used a (+) instead
e.g. odds of 4:1 –> we would need to do 1/(1+4) = 1/5 = 20%
How do you calculate the probability of A OR B?
When A and B are independent - p(A) + p(B)
When A and B can occur together - p(A) + p(B) - p(AandB)
How do you calculate probability of A AND B?
When A and B are independent - p(A) x p(B)
When A and B can occur together - p(A) x p(B|A) where p(B|A) is the conditional probability of B given that A has already happened
It is important to realise that p(A and B) IS NOT the same as p(B and A)
How do we calculate probability for complex (but still discrete) events?
Calculate probability DENSITY - probability of a particular outcome occurring
The cumulative distribution for that outcome represents the probability of all outcomes less than or equal to that outcome e.g. distribution for p(1head) is the density for 1 head plus the density for no heads
How is probability dealt with for continuous variables?
Talk more about probability of values within a range - we can produce curves under which the area represents the density function of an outcome
For example, the normal distribution is such a probability distribution curve
