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AP Statistics > Probability > Flashcards

Probability Flashcards

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

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

Rule 1. Legitimate Values

A

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

23
Q

Rule 2. Sample Space

A

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

24
Q

Rule 3. Complement

A

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

ex. Roll a fair die

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

25
Q

Rule 4. Addition

A

(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
Q

Rule 5. Conditional Probability

A

A probability that takes into account a given condition

27
Q

Independent

A
  • 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
Q

Rule 6. Multiplication

A

P(A and B) = P(A) * P(B|A)

if events A & B are indipendent

P(A and B)= P(A) * P(B)

29
Q

Rule 6. At Least One

A

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
Q

the collection of all possible outcomes of a chance experiment

A

Sample Space

31
Q

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

A

Sample Space of Rolling a Die

32
Q

any collection of outcomes from the sample space

A

Event

33
Q

E={2,3,5}

A

Rolling a Prime

34
Q

Consists of all outcomes that are not in the event

A

Complement

35
Q

EC={1,3,5}

A

Not Rolling an Even #

36
Q
  • the event A or B happening
  • consists of all outcomes that are in at least one of the two events
A

Union

37
Q

the probability of event A or B happening

A

P (A ∪ B)

38
Q

E={2,3,4,5,6}
E= {Prime ∪ Even}

A

Rolling a prime # or even #

39
Q
  • the even A and B happening
  • consists of all outcomes that are in both event
A

Intersection

40
Q

the probability of event A and B happening

A

P (A ∩ B)

41
Q

E={2 hearts, 2 diamonds}

E= (Red ∩ 2)

A

Drawing a red card and a “2”

42
Q
  • two events have no outcomes in common
  • these events are dependent because if one occurs the other can’t
A

Mutually Exclusive (disjoint)

43
Q
  • rolling a “2” and a “5”
  • drawing a Red card and a Black Card
A

Example of Disjoint Events

44
Q
A

Venn Diagram- Complement of A

45
Q
A

Venn Diagram- A or B (A∪B)

46
Q
A

Venn Diagram- (A ∩ B)

47
Q
A

Venn Diagram- Disjoint Events

48
Q
  • 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
A

Probability

49
Q
  • The relative frequency at which chance experiment occurs
  • flip a fair coin 30 times and get 17 heads (17/30)
A

Experimental Probability

50
Q
  • the likelihood an even will happen
  • Probability of heads on 1 toss= 1/2
A

Theoretical Probability

AP Statistics (2 decks)

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