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2021 AP STATISTICS > DECK 10: UNIT 4 - PROBABILITY TERMS AND CONCEPTS > Flashcards

DECK 10: UNIT 4 - PROBABILITY TERMS AND CONCEPTS Flashcards

1
Q

what is the law of large numbers?

A

guarantees that in the long run.. The relative frequency settles down to true probability.. (you’ll have 50% heads after an infinite number of coin flips with a fair coin)

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2
Q

What is a mistake that people make with the law of large numbers?

A

they make short term predictions. The law of large numbers talks about the LOOOOOOONG run relative frequency.

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3
Q

what is probability?

A

THE LONG RUN RELATIVE FREQUENCY!!

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4
Q

What is the “hot hand” view of probability?

A

Misrepresentation of the law of large numbers. If someone flipped a coin and it landed on heads 4 times in a row… you’d expect it to be heads again because “heads is hot”.. NOT TRUE..

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5
Q

What is the law of averages?

A

a misinterpretation of the law of large numbers. Using this law, if you flipped 4 heads in a row, you’d expect the next one to be a tails because it should even out in the long run, as if the coin remembers that it “owes you” something… NOT TRUE

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6
Q

A bag has 3 red chips and 4 blue chips.. WTPT you grab a red first, then put it back in and then grab a red again?

A

3/7 * 3/7 = 9/49 (indep events)

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7
Q

If we use a NORMAL model to approx a BINOMIAL.. What are mean and SD?

A

mean= np and sd= root(npq). So N (np, root(npq))

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8
Q

the (n over k) thing has a (5 over 2), how would you do it? What is it called?

A

Also known as “5 choose 2” or “5 C 2”..
5! / 3!2! (notice the bottom two add to the top)

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9
Q

WHAT ARE THE TWO INDEPENDENCE EQUATIONS USED FOR CHECKING?

A

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

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10
Q

How many ways can I arrange M N W Z ?

A

4! 4*3*2*1 = 24 ways

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11
Q

How to make TREES with screening tests????

A

SPLIT UP POPULATION FIRST >>>>>> then split the groups by outcomes of the test

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12
Q

What is a continuous probability function or curve?

A

A line or curve (like the normal model) that has an area of exactly one. The probability is found by finding the area between the boundaries given.

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13
Q

How to find P(at least 1)?

A

1-P(none)

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14
Q

Do we add or subtract st dev when combining models?

A

neither… you always just add variances. Square the st devs, add them, then take sqrt.

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15
Q

A bag has 3 red chips and 4 blue chips.. WTPT you reach in and grab 2 reds?

A

3/7 * 2/6 = 6/42 or 3/21 (notice the denominator changed)

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16
Q

What does mutually exclusive mean?

A

Same as disjoint.. Can’t both happen.

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17
Q

When can we use a NORMAL model to approx a binomial?

A

when np and nq are over 10

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18
Q

A bag has 3 red chips and 4 blue chips.. If you grab a red one on the first try and keep it, WTPT the next one is red?

A

2/6

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19
Q

can independent events be disjoint? EXPLAIN

A

NO, if they are independent, then knowing one doesn’t change the probability of the other, but if they are disjoint, knowing one makes the other impossible, so it does change the probability to 0

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20
Q

What is a probability distribution?

A

A table or graph showing all of the probabilites of certain occurances. THE PROBABILITIES HAVE TO ADD TO ONE!

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21
Q

what is independent?

A

when P(A)=P(A|B)… When the probability of A is the same even when B is also true… Knowing B does not affect the probability of A. (can also be checked by P(A)*P(B)=P(AandB))

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22
Q

You own a bike shop and order your tires from 2 companies (A and B). You order 80% from A and 20% from B. 1% of the tires from A are defective, while 4% from B are defective… What is the probability that a defective tire is from company A? How would you do this?

A

Tree diagram. Split up by company first, then use conditionals.
A BAD (.8)(.01)= .008
A GOOD (.8)(.99)= .792
B BAD (.2)(.04)= .008
B GOOD (.2)(.96)= . 192
It seems that .008/(.008+.008) or 50% are bad

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23
Q

when can you expect the first success? (mean of GEO)

A

1/p……… this tells you, on average, when the first success will occur….

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24
Q

what is representative?

A

It means that the sample statistics will be kind of like the population parameters.. The sample “looks like” the population.

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25
Q

what is a probability model?

A

a list of all possible values of random variable with respective probabilities. The probabilities should add to 1! Normal model is one…

26
Q

Does sample size matter, or percent of population?

A

Sample size. A sample of 150 will say as much about a population of 2,000 as it will about a population of 2,000,000. The sample size determines level of confidence and interval widths..

27
Q

What is area under ANY probability curve?

A

1 (or 100%)

28
Q

A bag has 3 red chips and 4 blue chips.. WTPT you reach in and first grab a blue and then grab a red?

A

4/7 * 3/6 = 12/42 or 6/21

29
Q

geocdf

A

(p,x)…. Probability of the FIRST SUCCESS being ON OR BEFORE the Xth trial.

30
Q

Why is it called “binomial”

A

These numbers come from the coefficients of expanded binomials.. (x+y)^1, (x+y)^2, (x+y)^3….

31
Q

What is “mutually exclusive?”

A

disjoint. Can’t happen at the same time.

32
Q

what is a complement?

A

the probability that it doesn’t happen. 1-P(it happens). (together they add to 100%) (P and Q are complements)

33
Q

what does geometric model tell us about

A

it is about FIRST SUCCESS… What is likelihood first success is on 5th trial?

34
Q

How do you write “A BINOMIAL MODEL WITH p=.35 and n=12?”

A

B(12, .35) B(N, P)

35
Q

what is disjoint?

A

can’t be joined…. They can’t both happen at the same time! (being over 5 feet and under 4 feet)

36
Q

binopdf

A

(n,p,x)….. Probability of exactly X successes in N trials. (PARTICULAR probability)

37
Q

What is “probability of at least one” the same as?

A

1-probability of NONE.

38
Q

how do you combine probability models?

A

add or subtract the means, and then ADD THE VARIANCES ALWAYS…

39
Q

what is pythagorean theorem of stats?

A

st dev of combined model is: sqrt(st dev squared + st dev squared) or more if you combine more…

40
Q

can disjoint events be independent? EXPLAIN

A

NO.. If they are disjoint then knowing one tells you that the other couldn’t happen so they are always NOT INDEPENDENT

41
Q

How do you find mean and sd of probability model?

A

put values in L1, probabilities in L2, and run “1-var stats L1,L2” and you get it!

42
Q

How do you do the tricky reverse tree problems (like test says pregnant.. What is probability you actually are?)

A

SPLIT UP POPULATION FIRST >>>>>> then split the groups by outcomes of the test.. BE SURE TO LABEL THE OUTCOMES and multiply the branches to the end… To find P(pregnant|test says pregnant), only look at the 2 branches that end with test saying pregnant.. put the actual pregnant over the sum of both pregnant and non.

43
Q

what is that (n over k) thing in the binomial equation?

A

n choose k it tells you how many ways you can choose k objects from a set of n things. The formula is n!/(n!(n-k)!) the two numbers on bottom add to the number up top. These are coefficients in expanded binomials and can also be found in Pascal’s Triangle

44
Q

What is probability first success is on 7th try?

A

qqqqqq p (q^6*p). (this is a GEO prob)

45
Q

A bag has 3 red chips and 4blue chips.. WTPT you grab a blue?

A

4/7

46
Q

A bag has 3 red chips and 4blue chips.. WTPT you grab a blue then a red? (without replacing)

A

4/7 * 3/6 (notice that there were only 6 in the bag)

47
Q

what is n! ?

A

it is “n factorial” example: 5! = 5*4*3*2*1= 120. tells you how many ways you can arrange n objects.

48
Q

What is the expected value?

A

The mean… What you’d AVERAGE if you played the game A LOT!!!!!!!!!

49
Q

How do you find the mean of a random variable if it is in a table?

A

values in L1, percents in L2, run 1-VAR STATS L1, L2.

50
Q

what does binomial model tell us about?

A

exactly x successes in K trials. What is likelihood of exactly 3 heads out of 13 flips?

51
Q

binocdf

A

(n,p,x)….. Probability of X OR LESS successes in N trials. (CUMULATIVE probability)

52
Q

What is the “mean of a random variable?”

A

The expected value… sum of probs times values

53
Q

geopdf

A

(p,x)… probability of FIRST SUCCESS being ON the Xth trial

54
Q

using calculator: suppose 30% of dogs have fleas. WTPT exactly 5 out of 12 have fleas?

A

binopdf(12, .30, 5)

55
Q

using calculator: suppose 30% of dogs have fleas. WTPT exactly 7 or less out of 20 have fleas?

A

binocdf (20, .30, 7)

56
Q

using calculator: suppose 30% of dogs have fleas. WTPT more than 10 out of 40 have fleas?

A

1 - 10 or less
1-binocdf(40, .30, 10)

57
Q

using calculator: suppose 30% of dogs have fleas. WTPT less than 4 out of 10 have fleas?

A

less than 4 is the same as 3 or less.
binocdf (10, .30, 3)

58
Q

using calculator: suppose 30% of dogs have fleas. WTPT no more than 8 out of 15 have fleas?

A

not more than 8 is the same as 8 or less.
binocdf(15, .30, 8)

59
Q

using calculator: suppose 30% of dogs have fleas. WTPT AT LEAST ONE OUT OF 10 has fleas?

A

1-none= 1-.7^10
or
1-binopdf( 10, .30, 0)
or
1-binocdf( 10, .30, 0)

60
Q

using calculator: suppose 30% of dogs have fleas. WTPT first dog with fleas was the fifth you checked?

A

not, not, not, not, yes… .7x.7x.7x.7x.3
or
geopdf (.30, 5

61
Q

using calculator: suppose 30% of dogs have fleas. WTPT first dog with fleas was ON OR BEFORE the fifth you checked?

A

geocdf (.30, 5)

62
Q

Packaging time. 10 min to find (sd=3) 15 min to box and wrap (sd=4), What is the mean and SD of entire process?

A

add means and add variances. Variances are sd^2.
mean= 10+15= 25min
var= 3^2+4^2= 9+16= 25
sd= sqrt var = sqrt 25 = 5
Mean= 25 and SD= 5

2021 AP STATISTICS (15 decks)

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