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2023 MIDTERM REVIEW > UNIT 4 - PROBABILITY TERMS AND CONCEPTS > Flashcards

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

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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8
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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9
Q

How many ways can I arrange M N W Z ?

A

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

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10
Q

How to find P(at least 1)?

A

1-P(none)

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11
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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12
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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13
Q

What does mutually exclusive mean?

A

Same as disjoint.. Can’t both happen.

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14
Q

What does disjoint mean?

A

Can’t both happen at the same time. A.K.A mutually exclusive. An animal can’t be a dog and a gorilla. They are mutually exclusive.

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15
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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16
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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17
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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18
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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19
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.

20
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…

21
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..

22
Q

What is area under ANY probability curve?

A

1 (or 100%)

23
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

24
Q

What is “mutually exclusive?”

A

disjoint. Can’t happen at the same time.

25
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)

26
Q

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

A

B(12, .35)

B(N, P)

27
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)

28
Q

binopdf (? ? ?) what are inputs?

A

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

29
Q

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

A

1-probability of NONE.

30
Q

how do you combine probability models?

A

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

31
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

32
Q

How do you find mean and sd of probability model? using L1 and L2?

A

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

33
Q

What is probability first success is on 7th try?

A

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

34
Q

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

A

4/7

35
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)

36
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.

37
Q

What is the expected value?

A

The mean OF THE RANDOM VARIABLE… What you’d AVERAGE if you played the game A LOT!!!!!!!!!

(multiply values times probabilities and add)

38
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.

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

What is the “mean of a random variable?”

A

The expected value… sum of probs times values

41
Q

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

A

binopdf(12, .30, 5)

42
Q

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

A

binocdf (20, .30, 7)

43
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)

44
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)

45
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)

46
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)

47
Q

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

A

no, no, no, no, yes… .7*.7*.7*.7*.3
or
geopdf (.30, 5)

2023 MIDTERM REVIEW (6 decks)

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