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2015 AP STATS > UNIT 4 PROBABILITY ALL > Flashcards

UNIT 4 PROBABILITY ALL Flashcards

1
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. The normal model is a probability model.

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2
Q

What is a probability distribution?

A

A table or graph showing all of the probabilites of certain occurances

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3
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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4
Q

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

A

4/7

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5
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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6
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

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7
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

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8
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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9
Q

What is probability first success is on 7th try?

A

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

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10
Q

what is n! ?

A

it is “n factorial” example: 5! = 54321= 120. tells you how many ways you can arrange n objects.

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11
Q

How many ways can I arrange M N W Z ?

A

4! 432*1 = 24 ways

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12
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!/(k!(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

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13
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?

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14
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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15
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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16
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)

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17
Q

what is disjoint?

A

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

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18
Q

What does mutually exclusive mean?

A

Same as disjoint.. Can’t both happen.

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19
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… IT IS NOT TRUE

20
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

21
Q

What is the “hot hand” view of probability?

A

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..

22
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

23
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. Height and IQ.

24
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)

25
Q

how do you combine probability models?

A

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

26
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!

27
Q

What is the “mean of a random variable?”

A

The expected value. sum of probabilitiess times values

28
Q

What is the expected value?

A

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

29
Q

what is probability?

A

THE LONG RUN RELATIVE FREQUENCY!!

30
Q

what does geometric model tell us about

A

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

31
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?.

32
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.

33
Q

geocdf

A

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

34
Q

How can we use Pascal’s Triangle?

A

To find probability of x successes in K trials.. BINOMIAL BABY!!!

35
Q

How to make TREES with screening tests????

A

SPLIT UP POPULATION FIRST&raquo_space;»» then split the groups by outcomes of the test

36
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&raquo_space;»» then split the groups by outcomes of the test.. BE SURE TO LABEL THE OUTCOMES. 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.

37
Q

what is the law of large numbers?

A

guarantees that in the long long 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)

38
Q

How to find P(at least 1)?

A

1-P(none)

39
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?

40
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

41
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..

42
Q

geopdf

A

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

43
Q

binopdf

A

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

44
Q

binocdf

A

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

45
Q

What is area under ANY probability curve?

A

1 (or 100%)

46
Q

What is “mutually exclusive?”

A

disjoint

2015 AP STATS (11 decks)

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