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AP Statistics > Probability > Flashcards

Probability Flashcards

(50 cards)

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1
Q

Sample Space

A

the collection of all possible outcomes of a chance experiment

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2
Q

Sample Space of Rolling a Die

A

S={1,2,3,4,5,6}

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3
Q

Event

A

any collection of outcomes from the sample space

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4
Q

Rolling a Prime

A

E={2,3,5}

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5
Q

Complement

A

Consists of all outcomes that are not in the event

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6
Q

Not Rolling an Even #

A

EC={1,3,5}

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7
Q

Union

A
  • the event A or B happening
  • consists of all outcomes that are in at least one of the two events
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8
Q

P (A ∪ B)

A

the probability of event A or B happening

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9
Q

Rolling a prime # or even #

A

E={2,3,4,5,6}
E= {Prime ∪ Even}

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10
Q

Intersection

A
  • the even A and B happening
  • consists of all outcomes that are in both event
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11
Q

P (A ∩ B)

A

the probability of event A and B happening

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12
Q

Drawing a red card and a “2”

A

E={2 hearts, 2 diamonds}

E= (Red ∩ 2)

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13
Q

Mutually Exclusive (disjoint)

A
  • two events have no outcomes in common
  • these events are dependent because if one occurs the other can’t
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14
Q

Example of Disjoint Events

A
  • rolling a “2” and a “5”
  • drawing a Red card and a Black Card
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15
Q

Venn Diagram- Complement of A

A
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16
Q

Venn Diagram- A or B (A∪B)

A
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17
Q

Venn Diagram- (A ∩ B)

A
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18
Q

Venn Diagram- Disjoint Events

A
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19
Q

Probability

A
  • The outcome of a chance process that describes the proportion of times the outcome would occur in a very long series of repetitions
  • P(Event)
  • P(E)= favorable outcomes/total outcomes
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20
Q

Experimental Probability

A
  • The relative frequency at which chance experiment occurs
  • flip a fair coin 30 times and get 17 heads (17/30)
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21
Q

Theoretical Probability

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A
  • the likelihood an even will happen
  • Probability of heads on 1 toss= 1/2
22
Q

Rule 1. Legitimate Values

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A

For any even E, 0_<P(E)<_1

23
Q

Rule 2. Sample Space

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A

If S is the sample space, P(S)=1

24
Q

Rule 3. Complement

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A

For any event E, P(E) + P(not E)=1

ex. Roll a fair die

P(not a 2)= 1-P(2)

25
**Rule 4.** Addition
(General) If two event E & F are not disjoints, P(E or F)= P(E) + P(F) - P(E&F) If the two events ARE Disjoint then P(E & F)= 0 thus P(E or F)= P(E) = P(F)
26
Rule 5. Conditional Probability
A probability that takes into account a given condition
27
Independent
* Two events are independent if knowing that one will occur (or has occurred) does not change the probability that the other occurs * DISJOINT EVENTS ARE NOT INDEPENDENT * Independent iff P(BIA)=P(B)
28
**Rule 6.** Multiplication
P(A and B) = P(A) \* P(B|A) if events A & B are indipendent P(A and B)= P(A) \* P(B)
29
**Rule 6.** At Least One
The probability that at least one outcome happens is 1 minus the probability that no outcomes happen P(at least 1)= 1- P(none)
30
the collection of all possible outcomes of a chance experiment
Sample Space
31
S={1,2,3,4,5,6}
Sample Space of Rolling a Die
32
any collection of outcomes from the sample space
Event
33
E={2,3,5}
Rolling a Prime
34
Consists of all outcomes that are not in the event
Complement
35
EC={1,3,5}
Not Rolling an Even #
36
* the event A or B happening * consists of all outcomes that are in at least one of the two events
Union
37
the probability of event A or B happening
P (A ∪ B)
38
E={2,3,4,5,6} E= {Prime ∪ Even}
Rolling a prime # or even #
39
* the even A and B happening * consists of all outcomes that are in both event
Intersection
40
the probability of event A ***_and_*** B happening
P (A ∩ B)
41
E={2 hearts, 2 diamonds} E= (Red ∩ 2)
Drawing a red card and a "2"
42
* two events have ***_no_*** outcomes in common * these events are ***_dependent_*** because if one occurs the other ***_can't_***
Mutually Exclusive (disjoint)
43
* rolling a "2" and a "5" * drawing a Red card and a Black Card
Example of Disjoint Events
44
Venn Diagram- Complement of A
45
Venn Diagram- A or B (A∪B)
46
Venn Diagram- (A ∩ B)
47
Venn Diagram- Disjoint Events
48
* The outcome of a chance process that describes the proportion of times the outcome would occur in a very long series of repetitions * P(Event) * P(E)= favorable outcomes/total outcomes
Probability
49
* The relative frequency at which chance experiment occurs * flip a fair coin 30 times and get 17 heads (17/30)
Experimental Probability
50
* the likelihood an even will happen * Probability of heads on 1 toss= 1/2
Theoretical Probability

AP Statistics (2 decks)

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