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Biostatistics > Probability > Flashcards

Probability Flashcards

1
Q

what is a random trial

A

process with two or more possible outcomes whose occurrence CANNOT be predicted with certainty

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2
Q

what are examples of random trials

A

rolling a dice

flipping a coin

random sample of population

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3
Q

event

A

any possible subset of ALL the possible outcomes of a random trial

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4
Q

what are the outcomes and events for a dice roll (

A

outcomes
- the possible numbers rolled (1, 2, 3, 4, 5, 6)

events include
- resulting exactly 6
- rolling all even
- rolling numbers add to 5

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5
Q

probability

A

the proportion of times an event would occur IF repeated random trials over and over IN THE SAME CONDITIONS

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6
Q

what is the notation for probability of event A

A

Pr[A]

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7
Q

what is the notation for probability of rolling a 5 on a dice

A

Pr[rolling a 5]

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8
Q

what must the probability for any event be

A

between 0 and 1 (inclusive)

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9
Q

how do venn diagrams represent probabilities visually

A

the area represents all possible outcomes of a random trial

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10
Q

mutually exclusive events

A

events that CANNOT occur at the same time

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11
Q

what are examples of mutually exclusive events

A

coin flip and dice rolls and having feathers + teeth

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12
Q

notation for “and” events

A

Pr[A and B]

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13
Q

what must mutually exclusive probabilities add to

A

ZERO

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14
Q

what kind of event does this show

A

mutually exclusive (no overlap between events)

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15
Q

probability distribution

A

a list of the probabilities of ALL mutually exclusive outcomes of a random trial

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16
Q

what kinds of values can a probability distribution be

A

discrete or continuous

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17
Q

discrete probability distribution

A

each outcome can only be defined by ONE value (like the combinations of two dice rolls adding to 7)

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18
Q

what is the probability of two dice rolls adding to 9? 7?

A

9
- there are four possible combinations to add to 9 and 36 total outcomes
4/36 = 0.11

7
- there are 6 possible combinations to add to 7 and 36 total outcomes
6/36 = 0.166

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19
Q

continuous probability distribution

A

there are almost infinite possibilities for values between two unique numbers because the variable can take any real number within that range

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20
Q

what is the probability of a variable in continuous probability distribution

A

basically zero

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21
Q

how do you find the probability of continuous data

A

on the curve, its the area under the graph

22
Q

what kind of probability distribution is this

A

continuous probability distribution

23
Q

what kind of probability distribution is this

A

discrete probability distribution

24
Q

notation for mutually exclusive events (or events)

A

Pr[A or B] = Pr[A] + Pr[B]

25
what must the sum be for mutually exclusive events
1
26
how to find the probability of an event NOT occurring in mutually exclusive events
1 - probability of event occurring
27
what is the GENERAL addition rule
Pr[A or B] = Pr[A] + Pr[B] - Pr[A and B]
28
when are events independent
if knowing probability of one event DOES NOT affect the probability of another event
29
what is an example of independent probability
rolling two dice (because the number on one dice will NOT affect the number on the other dice)
30
multiplication rule
probability that both independent events occur = product of the probability of each event
31
when does this rule apply
for independent events
32
when does this rule apply
addition rule - for when events are mutually exclusive
33
what does this rule apply
for mutually exclusive events and trying to find the opposite of the probability A
34
what are events if they are NOT independent
dependent
35
what does dependence of events suggest
that the variables are associated
36
what type of variable serves as a null hypothesis
independent events/variables
37
OR probabilities imply
addition
38
when do we use addition
when events are MUTUALLY EXCLUSIVE
39
when do we use multiplication rule
when A and B are INDEPENDENT
40
what does AND imply
multiplication rule
41
how do you find the probability of an event multiple times (say not rolling a 6 ten times in a row)
find the prob you want (not rolling 6 on a dice) and calculate it to the power of 1o (the number of times you are doing the trial in a row)
42
what are probability trees
a tool to assist in calculating the probability of events that consist of multiple random trials
43
when are probability trees helpful
when trying to ensure all possible sequences of events have been considered
44
probability that two children yields a boy and girl
there are two paths for the children being of different sexes - having a boy than girl (prob is 0.250) - having a girl than boy (0.250) - given that events are mutually exclusive, add each probability - there is a 0.500 chance of having two children boy and girl
45
dependent events
variables or events that are ASSOCIATED meaning they depend on each other to happen
46
conditional probability
the probability of that event occurring GIVEN THAT a condition is met
47
what does this notation mean
the probability of event A occurring given that the condition of B is met
48
what is the law of total probability
to find the overall probability of a particular event = sum its probability across EVERY possible condition weighted by the probability of that condition
49
general multiplication rule
Pr[A and B] = Pr[A] Pr{A|B] = Pr[B] Pr[A|B]
50
Bayes' theorem
51
why is Bayes' theorem useful
because you can use one conditional probability to determine the other

Biostatistics (9 decks)

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