Chpt 4 - Probability Flashcards
What is probability?
The measure of likeliness that a certain result of a chance experiment occurs
What is a chance experiment?
A process producing outcomes that vary randomly when repeated
What is the measure of likeliness that a certain result of a chance experiment occurs?
Probability
What is a process producing outcomes that vary randomly when repeated?
Chance experiment
What is an elementary outcome of a chance experiment called?
The sample point
What are the sample points of flipping a coin?
Head and tail
What is the collection of all sample points of a chance experiment called?
A sample space
What is the sample space denoted by?
capital S
What is the sample space when flipping a coin?
{head, tail}
What is the sample space when flipping 2 coins?
{HH, HT, TH, TT}
What is an event?
A specified result that may or may not occur
Such as flipping a coin and getting heads
How can an event be written out?
Give an example of flipping 2 coins and getting at least one head
A collection of outcomes
A = {HH, HT, TH}
Where A is the event, such as flipping a head, and the data within the brackets are possible outcomes in that event
What is the collection of outcomes for rolling higher than a 4 on a six sided dice?
A = {5, 6}
What is the probability of an event? Why is this difficult?
It’s the relative frequency of the event in a population
Remember it’s next to impossible to obtain the population data, so instead we use a sample
What is the range for a probability of an event
0 to 1
0 = an event that NEVER occurs
1 = an event that ALWAYS occurs
What is the f/N rule and why do we use it?
Assumes that the sample space has N sample points and these sample points are equally likely.
We use it because getting the entire population information needed for a relative frequency is difficult if not impossible to obtain, so as long as the sample is representative of the population we use a sample space
How do we denote a probability of event D?
P(D)
For event F, what is the probability of tossing 2 quarters and having the second toss be the same?
S = {HH, HT, TH, TT}
A = {HH, TT}
P(A) = 2/4 -> 1/2 or 0.5
What can we apply to events to produce new events?
Set operations
What is the complement set operation and what denotes it?
The complement of A is a set that includes sample points that are NOT in A but in the sample space S
It is denoted as notA or Ac (with the c superscript)
What is the intersection set operation and what denotes it?
The intersection of events A and B is a set that includes sample points that belong to BOTH A and B.
It is denoted as A&B or A ⋂ B
What is the union set operation and what denotes it?
The union of A and B is a set that includes sample points that are in A or B
It is denoted as AorB or A ⋃ B
What set operation is anything in a sample space that is not included within event A?
What is it denoted as?
Complement
It is denoted as notA or Ac (with the c superscript)
What set operation is anything that is included in only the overlapping area of 2 events (like the middle part of a Venn diagram)
What is it denoted as?
Intersection
It is denoted as A&B or A ⋂ B
What set operation is anything that is included in the entire A and B circles of a Venn diagram?
What is it denoted as?
Union
It is denoted as AorB or A ⋃ B
You are rolling a fair die. Event A is any number on the upper face less than 5 and event B is any number on the upper face more than 3 but less than 6.
What is the sample space of tossing the die?
S = {1, 2, 3, 4, 5, 6}
You are rolling a fair die. Event A is any number on the upper face less than 5 and event B is any number on the upper face more than 3 but less than 6.
What is event A? What is event B?
A = {1, 2, 3, 4}
B = {4, 5}
You are rolling a fair die. Event A is any number on the upper face less than 5 and event B is any number on the upper face more than 3 but less than 6.
What is in the complement of event A?
notA = {5, 6}
You are rolling a fair die. Event A is any number on the upper face less than 5 and event B is any number on the upper face more than 3 but less than 6.
What is in the union of A and B?
A ⋃ B = {1, 2, 3, 4, 5}
This is AorB
You are rolling a fair die. Event A is any number on the upper face less than 5 and event B is any number on the upper face more than 3 but less than 6.
What is the intersection of A and B?
A ⋂ B = {4}
This is A&B
There are 4 rabbits and 4 goats on a farm and 4 are chosen at random to be sent to the zoo. Suppose you observe the number of rabbits.
What is the sample space?
S = {0, 1, 2, 3, 4}
(remember we are only counting rabbits…if there are 0 rabbits going, then there are 4 goats going; 3 rabbits would result in 1 goat going)
There are 4 rabbits and 4 goats on a farm and 4 are chosen at random to be sent to the zoo. Suppose you observe the number of rabbits.
Event A has at least half the chosen animals as rabbits; event B is at least half the goats chosen.
What are the 2 events?
A = {2, 3, 4}
B = {0, 1, 2,}
Remember we are still only looking at rabbits, so if there is 1 rabbit, then 3 goats are going
There are 4 rabbits and 4 goats on a farm and 4 are chosen at random to be sent to the zoo. Suppose you observe the number of rabbits.
Event A has at least half the chosen animals as rabbits; event B is at least half the goats chosen.
What is the union of these events?
AorB = {0, 1, 2, 3, 4}
Remember we are still only looking at rabbits, so if there is 1 rabbit, then 3 goats are going
This is A ⋃ B
There are 4 rabbits and 4 goats on a farm and 4 are chosen at random to be sent to the zoo. Suppose you observe the number of rabbits.
Event A has at least half the chosen animals as rabbits; event B is at least half the goats chosen.
What is the intersection of these events?
A&B = {2}
Remember we are still only looking at rabbits, so if there is 1 rabbit, then 3 goats are going
This is A ⋂ B