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IB APPLICATIONS > PROBABILITY > Flashcards

PROBABILITY Flashcards

1
Q

What is probability?

A

The likelihood of an event happening.

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2
Q

What is the the difference between theoretical and experimental probability?

A

theoretical is from thinking of all of the possibilities and doing it with math, experimental is the #successes/total attempts you observe.

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3
Q

how do you find “probability”

A

(# ways you can be successful) / (# total ways possible)

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4
Q

What is the symbol that joins two sets together into one set?

A

A big U , stands for UNION

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5
Q

What is the symbol that just takes the overlap of two sets?

A

An upside down U, look like this: ∩, INTERSECTION

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6
Q

What do students forget about OR ?

A

The OR BOTH part. The union of A and B are all of the elements in A, in B and also the ones that are in BOTH.

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7
Q

Why does OR go with UNION, ex. A U B = A or B

A

Because you are part of the union as long as you are a part of A or B or BOTH.

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8
Q

Why does AND go with INTERSECTION? A ∩ B = A and B

A

Because ONLY if you are a member of A and also a member of B, can you be a part of the intersection, A ∩ B

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9
Q

OR goes with______ [union or intersection]

A

union

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10
Q

AND goes with ______ [union or intersection]

A

intersection

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11
Q

UNION goes with ______ [OR or AND]

A

OR

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12
Q

INTERSECTION goes with _____ [OR or AND]

A

AND

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13
Q

What numbers can represent a probability?

A

Always between 0 and 1, examples: 0, .75, .05, 1, .35

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14
Q

What fractions can represent a probability?

A

Any fraction as long as the top is smaller than the bottom (or equal). IT CAN’T BE TOP HEAVY!

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15
Q

Can you have a probability of 3.5?

A

NO. probabilities are between 0 and 1

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16
Q

can you have a probability of 0.5?

A

Yes, that’s 50%

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17
Q

can you have a probability of 3/5?

A

Yes, that’s 60%

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18
Q

can you have a probability of 5/3?

A

NO… that is more than 1

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19
Q

How can you think of %

A

PER 100 (or, divided by 100)

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20
Q

If you have 3 pairs of shoes, two pairs of pants and 4 shirts.. how many outfits?

A

3*2*4= 24 outfits

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21
Q

How many cards in a deck of cards?

A

52

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22
Q

How many diamonds in a deck of cards?

A

13

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23
Q

What is the probability of randomly taking one card and getting a diamond from a deck?

A

13/52 or 1/4

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24
Q

What is the probability of randomly taking one card and getting a king from a deck?

A

4/52 or 1/13

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25
Q

What is the probability of randomly taking one card and getting a red card from a deck?

A

26/52 or 1/2

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26
Q

How many kings in a deck of cards?

A

4

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27
Q

what is the probability of getting 3 tails in a row flipping a coin?

A

1/2 x 1/2 x 1/2 = 1/8

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28
Q

What does A’ mean?

A

The elements not in A

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29
Q

If A = { 1, 2 }, how many elements does A have?

A

two

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30
Q

If A = { 1, 2, 6} , what is n(A) ?

A

the number of elements in A. In this case, n(A)= 3

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31
Q

Difference between a Permutation and a Combination?

A

Permutation is choosing and Placing in a Particular Place, Combinations are just choosing

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32
Q

where is the permutation button on the calculator?

A

Math > PRB then down to nPr

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33
Q

where is the combination button on the calculator?

A

Math > PRB then down to nCr

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34
Q

if there are 10 kids and you are choosing 3 to bring on a trip, how many ways can you do that?

A

Combination. nCr with n=10 and r=3

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35
Q

If there are 10 kids and you are choosing a president, vp and treasurer, how many ways can you do that?

A

Permutation. nPr with n=10 and r=3

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36
Q

With tree diagrams, what does MA.AD stand for?

A

Multiply across, Add down

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37
Q

What do the probabilities on the branches leaving a single node in a tree diagram have to add to?

A
  1. If you have two branches, then they should add to 1, if you have five branches from same node, all five added together should equal 1.
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38
Q

How do you get the probability of taking a certain route on a tree diagram?

A

multiply the branches along the path till the end. write it at the end of the branch.

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39
Q

when you are given a two way table, what should you always do?

A

PUT IN THE TOTALS ON SIDE and BOTTOM and the OVERALL TOTAL IN THE CORNER

40
Q

What is a way to help shading in VENN diagrams?

A

Label the areas 1, 2, 3 and 4. Let A= {1,2} B= {2,3} , intersection is {2} and outside of the circles {4).

41
Q

When you shade a VENN diagram, what does A U B look like?

A

Both circles and the overlap are all shaded (everything inside)

42
Q

When you shade a VENN diagram, what does A ∩ B look like?

A

Just the overlap sliver in the middle is shaded.

43
Q

What does (A’)’ look like when shading?

A

double negative. (A’)’ = A, so the entire A circle should be shaded.

44
Q

What does (A U B)’ look like when shading?

A

shade just the area outside of the circles.

45
Q

change the probability of 1/3 to a decimal and a percent

A

about .33 or 33% (.33333333333)

46
Q

change the probability of 2/3 to a decimal and a percent

A

about .67 or 67% (.66666666666)

47
Q

change the probability of 1/2 to a decimal and a percent

A

0.5 or 50%

48
Q

change the probability of 1/4 to a decimal and a percent

A

0.25 or 25%

49
Q

change the probability of 3/4 to a decimal and a percent

A

0.75 or 75%

50
Q

change the probability of 1/5 to a decimal and a percent

A

0.2 or 20%

51
Q

change the probability of 2/5 to a decimal and a percent

A

0.4 or 40%

52
Q

change the probability of 3/5 to a decimal and a percent

A

0.6 or 60%

53
Q

change the probability of 4/5 to a decimal and a percent

A

0.8 or 80%

54
Q

change the probability of 1/8 to a decimal and a percent

A

0.125 or 12.5%

55
Q

change the probability of 1/10 to a decimal and a percent

A

0.1 or 10%

56
Q

change the probability of 0.45 to a percent

A

45%

57
Q

change the probability of 6% to a decimal

A

0.06

58
Q

change the probability 0.0003 to a percent

A

0.03%

59
Q

change the decimal 0.3 to a fraction

A

3/10

60
Q

change the decimal 0.03 to a fraction

A

3/100

61
Q

change the decimal 0.003 to a fraction

A

3/1000

62
Q

change the decimal 0.0003 to a fraction

A

3/10000

63
Q

change the probability 0.04% to a decimal

A

0.0004

64
Q

change the probability 0.04 to a percent

A

4%

65
Q

change the probability 0.5% to a decimal

A

0.005

66
Q

change the probability 40% to a decimal

A

0.4

67
Q

change the probability 5% to a fraction

A

1/20 (one out of 20)

68
Q

one out of five is ____ or ____%

A

0.20 or 20%

69
Q

one out of ten is _____ or ____%

A

0.1 or 10%

70
Q

three out of ten is ____ or ____%

A

0.3 or 30%

71
Q

one out of twenty is ____ or _____%

A

0.05 or 5%

72
Q

one out of four is _____ or ____%

A

0.25 or 25%

73
Q

one out of three is ____ or ____%

A

about .33 or 33%

74
Q

two out of three is ____ or ____%

A

about .66 or 66%

75
Q

two out of five is ____ or ____ %

A

0.4 or 40%

76
Q

three out of five is ____ or ____%

A

0.6 or 60%

77
Q

four out of five is ____ or ____%

A

0.8 or 80%

78
Q

change the probability 0.8 to a percent and a fraction

A

80% and 4/5

79
Q

what are the decimal equivalents of these popular fractions: 1/2, 1/3, 1/4, 1/5, 1/8, 1/10, 1/100, 1/1000

A

0.5 , 0.333, 0.25, 0.2, 0.125, 0.1, 0.01, 0.001

80
Q

What are the fractional equivalents of these popular decimals: 0.5 , 0.333, 0.25, 0.2, 0.125, 0.1, 0.01, 0.001

A

1/2, 1/3, 1/4, 1/5, 1/8, 1/10, 1/100, 1/1000

81
Q

What are the fractional equivalents of these popular percents: 50%, 33.3%, 25%, 20%, 12.5%, 10%, 1%, 0.1%

A

1/2, 1/3, 1/4, 1/5, 1/8, 1/10, 1/100, 1/1000

82
Q

What are the decimal equivalences of these popular percents? 50%, 33.3%, 25%, 20%, 12.5%, 10%, 1%, 0.1%

A

0.5 , 0.333, 0.25, 0.2, 0.125, 0.1, 0.01, 0.001

83
Q

How can centimeters and a meter stick help you think of percent?

A

Think of centimeters as “PERCENTIMETERS”.. each one is one percent of a meter. 35cm is 35% of a meter.

84
Q

Can you have a percent of 5/4?

.

A

YES! that would be 125%….. (this can’t be a probability)

85
Q

how can you think of 150% of something?

A

150% of a pizza is one and a half pizzas!! (this can’t be a probability)

86
Q

can you have more than 100% of something?

A

YES…. if you have more than a whole. (but this can’t be a probability)

87
Q

change the decimal 0.3 to a percent.

A

30%

88
Q

change the decimal 0.03 to a percent.

A

3%

89
Q

change the decimal 0.003 to a percent.

A

0.3%

90
Q

change the decimal 0.0003 to a percent.

A

0.03%

91
Q

how could you change 25/52 into a decimal?

A

use your calculator, just divide: 25/52=

(multiply by 100 to get the percent)

92
Q

If you have a decimal and want the percent, what can you do on your calculator?

A

multiply the decimal by 100. that will give you the percent.

93
Q

If you have a percent and want the decimal, what can you do?

A

on your calculator, divide the percent by 100 and you will get the decimal.

94
Q
A
95
Q

if you have a percent, like 32% and want a fraction, what can you do?

A

just write it over 100..

so 32% = 32/100

or “thirty-two hundredths”

96
Q
A

IB APPLICATIONS (5 decks)

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