probability Flashcards
what does probability study
Probability studies randomness and is a quantity between 0 and 1, sometimes expressed as a percentage.
what are proportions
A number, amount, or level of one thing when compared to another, expressed between [0,1] or as a percentage.
How is mathematical probability calculated?
By dividing the number of favorable outcomes by the total number of possible outcomes.
The total number of possible outcomes is the sample space.
what is empirical probability
The proportion of favourable outcomes observed in a sample .
what is relative frequency
The proportion of favorable outcomes in a sample, approaching a limit as sample size increases.
As sample size increases, the relative frequency will reach a limit.
what is the complement rule
The probability of an event NOT occurring is:
Pr(πβ²)=1βPrβ‘(π)
What is the probability of rolling a 6 on a fair six-sided die?
1/6
multiplication rule
For two independent events π and π, the probability of of both occurring is: ππ(πβ©π)=ππ(π)Γππ(π)
What is the probability of flipping a Head AND rolling a 6?
ππ(πβ©π) = 1/2 x 1/6 = 1/12
what does it mean if events X and Y are independent
If π and π are independent one event does not influence another.
what does β© stand for
AND
What is the addition rule in probability?
The probability of event π OR event Y OR BOTH occurring is:
ππ(πβͺπ)=ππ(π)+ππ(π)βππ(πβ©π)
What is the probability of flipping a Head OR rolling a 6 OR both?
ππ(πβͺπ)= 1/2 + 1/6 - 1/12 = 7/12
what does βͺ mean
union
a OR b
BOTH a & b
what does it mean if events X and Y are not mutually exclusive
the two events can happen together
What are mutually exclusive events?
events that cannot occur at the same time. For example, a coin cannot show both heads and tails at the same time.
P(Xβ©Y)=0
if events X and Y are mutually exclusive what happens to the multiplication and addition rule
ππ(πβ©π)=0
ππ(πβͺπ)=ππ(π)+ππ(π)
what is conditional probabilitiy
Conditional probability is the probability of event π΄ occurring given that event π΅ has already occurred
formula for conditional probability
ππ(π|π) = ππ(πβ©π) / ππ(π)
How do you calculate the probability of two dependent events?
ππ(πβ©π)=ππ(π|π)Γππ(π)
what are non independent events
If π and π are independent then ππ(π|π)=ππ(π)
what is bayes theorum
Bayesβ Theorem provides a way to update the probability of an event based on new information:
ππ(π|π) = [ππ(π|π)ππ(π)] / ππ(π)
how to convert numbers to proportions
divide by the total sample
What is marginal probability?
Marginal probability is the probability of an event occurring, regardless of other variables.
