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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
Q

what must the sum be for mutually exclusive events

A

1

26
Q

how to find the probability of an event NOT occurring in mutually exclusive events

A

1 - probability of event occurring

27
Q

what is the GENERAL addition rule

A

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

28
Q

when are events independent

A

if knowing probability of one event DOES NOT affect the probability of another event

29
Q

what is an example of independent probability

A

rolling two dice (because the number on one dice will NOT affect the number on the other dice)

30
Q

multiplication rule

A

probability that both independent events occur = product of the probability of each event

31
Q

when does this rule apply

A

for independent events

32
Q

when does this rule apply

A

addition rule - for when events are mutually exclusive

33
Q

what does this rule apply

A

for mutually exclusive events and trying to find the opposite of the probability A

34
Q

what are events if they are NOT independent

A

dependent

35
Q

what does dependence of events suggest

A

that the variables are associated

36
Q

what type of variable serves as a null hypothesis

A

independent events/variables

37
Q

OR probabilities imply

A

addition

38
Q

when do we use addition

A

when events are MUTUALLY EXCLUSIVE

39
Q

when do we use multiplication rule

A

when A and B are INDEPENDENT

40
Q

what does AND imply

A

multiplication rule

41
Q

how do you find the probability of an event multiple times

(say not rolling a 6 ten times in a row)

A

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
Q

what are probability trees

A

a tool to assist in calculating the probability of events that consist of multiple random trials

43
Q

when are probability trees helpful

A

when trying to ensure all possible sequences of events have been considered

44
Q

probability that two children yields a boy and girl

A

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
Q

dependent events

A

variables or events that are ASSOCIATED meaning they depend on each other to happen

46
Q

conditional probability

A

the probability of that event occurring GIVEN THAT a condition is met

47
Q

what does this notation mean

A

the probability of event A occurring given that the condition of B is met

48
Q

what is the law of total probability

A

to find the overall probability of a particular event = sum its probability across EVERY possible condition weighted by the probability of that condition

49
Q

general multiplication rule

A

Pr[A and B] = Pr[A] Pr{A|B] = Pr[B] Pr[A|B]

50
Q
A

Bayes’ theorem

51
Q

why is Bayes’ theorem useful

A

because you can use one conditional probability to determine the other

Biostatistics (9 decks)

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