Chapter 5 Flashcards
what letter represents a probability set?
S
what is the law of large numbers?
when an experiment is performed many, many times, the relative frequency of an event tends to become closer to the actual probability
what is the union of two events?
the set of elements in either A or B
the probability that A, B, or both will occur
what is the union of two events denoted as?
AUB
what is the intersection of two events?
the set of elements in both A and B
the probability that both events will occur
what is the intersection of two events denoted as?
A∩B
what is a complement to an event?
the probability of the event not occurring
how can you find the complement to an event?
1 - the probability
what is the complement to an event denoted as?
P(A’) or P(A^c)
what is an “and” probability?
an intersection probability
how do you calculate an “and” probability?
P(A) x P(B) = P(A∩B)
P(A|B) x P(B) = P(A∩B)
what is an “or” probability?
a union probability
how do you calculate an “or” probability?
P(A) + P(B) - P(A∩B) = P(AUB)
t/f: for mutually exclusive events, P(A∩B) = 0 (explain why if this is false)
true (the two events cannot occur simultaneously, therefore there is no intersection)
what are independent events?
events where knowing that one event occurs does not change the probability of the other one occurring
example: flipping a coin
how do you test for independence?
P(A|B) = P(A)
this shows that B had no effect
P(B|A) = P(B)
this shows that A had no effect
P(A∩B) = P(A) x P(B)
what are conditional events?
the probability of one event occurring given that the other event occurs
how do you find the probability of a conditional event?
P(A|B) = P(A∩B) / P(B)
t/f: disjointed is not another way to say mutually exclusive
false: it is another way to say mutually exclusive
what are mutually exclusive events?
events that have no outcomes in common and can never occur simultaneously
example: flipping both heads and tails at the same time
what are the first branches of a tree diagram called?
unconditional probabilities
what are the second branches of a tree diagram called?
conditional probabilities
what are the third branches of a tree diagram called?
joint probabilities
t/f: the joint probabilities of a tree diagram must add up to 1
true
how do you find a joint probability?
multiply the unconditional and conditional probabilities
if you had a tree diagram about gender and owning/not owning a dog, how would you find the probability of owning a dog?
add the joint probabilities of owning a dog
how are “given” probabilities calculated using a tree diagram?
usually, it is a joint probability divided by an unconditional probability, but this can be reversed
how should you start with venn diagrams?
if possible, fill in the middle/intersection part (the “and” probability) first
