New UNIT 4A

Question 1

What is area under ANY probability curve?

Answer 1

1 (or 100%)

Question 2

How to find P(at least 1)?

Answer 2

1-P(none)

Question 3

How many ways can you choose 3 books to take with you on a trip out of the 7 books on the shelf?

Answer 3

7 choose 3. 7!/(3! * 4!) notice that the two factorials on bottom add to the top.

Question 4

What is the law of averages?

Answer 4

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. Not true, 5 flips is not the long run. Infinity is. The next flip still has a 50% chance of being another head. You may hear someone say “he’s do for a hit” or “it’s bound to rain soon” both bad.

Question 5

What is the “hot hand?”

Answer 5

a misinterpretation of the law of large numbers. Using this law, if you flipped 4 tails in a row, you’d expect the next one to be another tails, because tails is “hot.” A baseball player who gets three hits in a row, you expect another hit? wrong. Streaks happen randomly.

Question 6

Probability of THIS OR THAT?

Answer 6

ADD P(this) + P(that) works when disjoint only, when not, subtract overlap.

Question 7

what is disjoint?

Answer 7

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

Question 8

Probability of THIS AND THAT?

Answer 8

Multiply P(this)*P(that) works when independent only, when not, then P(that) should be p (that|this)

Question 9

When to use general mult and what is it?

Answer 9

AND probability. Use when associated. P(this)*P(that|this). (IT ALWAYS WORKS FOR ALL SITUATIONS. When indep, the P(that|this) = P(that). So you end up with the simpler independent version)

Question 10

When to use general add and what is it?

Answer 10

OR probability. Use when not disjoint. (subtract overlap) P(this OR that) = P(this)+P(that) - P(this and that) (IT ALWAYS WORKS IN ALL SITUATIONS, when disjoint, P(this and that)= 0, so you end up with the simpler disjoint version)

Question 11

what is the law of large numbers?

Answer 11

states that in the long run.. (NOT SHORT 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)

Question 12

what is n! ?

Answer 12

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

Question 13

what is representative?

Answer 13

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

Question 14

probability this AND that . Add or multiply?

Answer 14

MULTIPLY

Question 15

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

Answer 15

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

Question 16

can independent events be disjoint? EXPLAIN

Answer 16

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 of the other to 0

Question 17

can disjoint events be independent? EXPLAIN

Answer 17

NO.. If they are disjoint then knowing one tells you that the other couldn’t happen so they are always NOT INDEPENDENT? or DISJOINT EVENTS ARE ALWAYS ASSOCIATED!!

Question 18

Probability this OR that when they are not disjoint? How?

Answer 18

probability A plus probability B minus the double counted (the ones that are both A and B) called “general addition rule”

P(A)+P(B)-P(A and B)

P(this)+P(that)-P(this and that)

Question 19

probability this and that when they are not independent? How?

Answer 19

probability A times probability B (knowing A is true) called general multiplication rule

P(A)*P(B given A)

P(this)*P(that given this)

Question 20

What is “mutually exclusive?”

Answer 20

same as disjoint

Question 21

How to find likelihood of being pregnant, given the test says you are? (tree)

Answer 21

Split population by %pregnant and %not who take test, then each of those into what test says. Then look just the groups that the test said pregnant. Then find: %pregnant/(total percent in both groups).

Question 22

How to make TREES with screening tests????

Answer 22

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

Question 23

what is probability?

Answer 23

THE LONG RUN RELATIVE FREQUENCY!!

Question 24

what is a complement?

Answer 24

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

Question 25

what is independent? What are the two equations to test for independence?

Answer 25

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

When the probability of A is the same even when B is also true. Knowing B does not affect the probability of A.

Question 26

How many ways can I arrange 4 letters?

Answer 26

4!

4*3*2*1= 24 ways

Question 27

What is the area under the normal curve?

Answer 27

1 or 100%

Question 28

What do we call it when two things can’t happen at the same time?

Answer 28

disjoint OR mutually exclusive

Question 29

what does binomial model tell us about?

Answer 29

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

Question 30

What is it called when knowing one event happened does not change the probability of another event occuring?

Answer 30

independent events

Question 31

What is probability first success is on 7th try?

Answer 31

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

Question 32

What is more important, percent of population or size of sample?

Answer 32

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..

Question 33

Give three examples of independent variables

Answer 33

1. Being tall and having a high GPA
2. If it is snowing and whether it is a Thursday or not
3. Whether a person likes pizza and their gender

(notice, knowing one bit of information does not impact the likelihood of the other being true also)

Question 34

Give three examples of variables that are not independent (associated)

Answer 34

1. Playing video games and gender (Knowing male makes it more likely they play)
2. Whether it is snowing and the month you are in (some months are more rainy than others, knowing what month changes likelihood of snowing)

3 If a pet is a dog and if it is a cat (knowing it is a dog makes it certain that it is not a cat).

(notice, knowing one bit of information changes the likelihood of the other being true also).

Question 35

Give three examples of disjoint events

Answer 35

1. A card being a CLUB and a RED
2. A student being a SENIOR and a FRESHMAN
3. An animal being a CAT and a GOLDFISH

(both can’t be true)

Question 36

Give three examples of events that are not mutually exclusive

Answer 36

1. Being a DOG and being SMELLY
2. Being a FRESHMAN and being FEMALE
3. Liking ICE CREAM and liking HAMBURGERS

(both can be true simultaneously)

Question 37

What do we call it when events are not independent?

Answer 37

associated

Question 38

what do we call it when events are not associated?

Answer 38

independent

Question 39

Do we say things are “dependent?”

Answer 39

NO! we say associated