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Definitions
Rules
Independence and Conditional Probability
Venn Diagrams (must be done in order)
Tree Diagrams (must be done in order)
100
A list of all possible outcomes.
What is sample space?
100
Possible probability values.
What is 0 <= p <= 1?
100
The conditional probability formula.
What is P(A|B) = P(A and B)/P(B)
100
Karen has applied to both Princeton and Stanford. According to her counselor, the probability that Princeton will admit her is 0.4, the probability that Stanford will admit her is 0.5 and the probability that both will admit her is 0.2. Jacob says the counselor is wrong because that makes a total probability of 1.1. True or false: Jacob is correct. Justify your answer with a Venn Diagram.
What is False, because Jacob is not remembering to account for the overlap of 0.2.
100
When tree diagrams are most useful.
What is when there is a series of 2 to 3 choices.
200
A subset of some of the possible outcomes.
What is an event?
200
The probability of mutually exclusive events happening at the same time.
What is zero?
200
The probability of simultaneous independent events.
What is P(A and B) = P(A) x P(B)
200
Karen has applied to both Princeton and Stanford. According to his counselor, the probability that Princeton will admit her is 0.4, the probability that Stanford will admit her is 0.5 and the probability that both will admit her is 0.2. The probability that neither university accepts her.
What is 0.3?
200
Many employers require applicants to take a drug test. A positive result indicates drug use, but a "false positive" where a non-drug user tests positive is a possibility. This happens about 5% of the time. A "false negative" occurs when a drug user shows as a non-drug user. This happens about 10% of the time. 4% of applicants are drug users. Draw a tree diagram of this situation.
What is (teacher will draw)?
300
The long run relative frequency of a chance outcome.
What is probability?
300
The complement rule.
What is P(Ac) = 1 - P(A)
300
This table represents the political party and gender of US Senators in a recent year.
Male Female
Republican 37 4
Democrat 48 11
Write the probability statement and find the probability of a randomly selected senator being a Democrat given that he is a male.
What is P(Democrat|Male) = 48/85?
300
Karen has applied to both Princeton and Stanford. According to her counselor, the probability that Princeton will admit her is 0.4, the probability that Stanford will admit her is 0.5 and the probability that both will admit her is 0.2. The probability that at least one of the universities will accept her.
What is 0.7?
300
For the previous situation, P(took drugs|positive test). Show your work.
What is 0.429?
400
An imitation of chance behavior, most often carried out with random numbers.
What is simulation?
400
The General Addition Rule.
What is P(A or B) = P(A) + P(B) - P(A and B)
400
This table represents the political party and gender of US Senators in a recent year.
Male Female
Republican 37 4
Democrat 48 11
Determine if male and Democrat are independent. Justify your answer.
What is no because P(Democrat) x P(male) not equal to P(D and M)? 59/100 x 85/100 not equal to 48/100.
400
This table represents the political party and gender of US Senators in a recent year.
Male Female
Republican 37 4
Democrat 48 11
Draw a Venn Diagram of the information in the table.
Teacher draws answer.
400
1000 applicants are tested. Turn your tree diagram into a table, include totals.
What is
Drugs No Drugs Total
Test Positive 36 48 84
Test Negative 4 912 916
Total 40 960 1000
500
A rule that the proportion of times that a particular outcome occurs in many repetitions approaches a single number.
What is the Law of Large Numbers?
500
Events that are mutually exclusive are (always, sometimes, never) independent.
What is never?
500
You roll a green die and a red die. Are the events S:{sum of seven} and F:{green 4} independent? Justify your answer.
What is yes because P(S|F) = P(S) = 0.1667?
500
This table represents the political party and gender of US Senators in a recent year.
Male Female
Republican 37 4
Democrat 48 11
Find P(Republicanc and Femalec)
What is 48/100, the probability that a senator is a male democrat?
500
For the previous question, what is the probability that a person who is using drugs will not test positive for drugs?
What is 4/1000?