applied mathematics - unit 4: probability in the social science

what is the probability that 1 out of 3 homeowners in the city are members of the neighborhood watch?

approximately 0.4084

lesson 19

binomial models for probability in the social sciences

lesson 16

combination in social science experiments and studies

which of the statements are true? select all that apply.

each trial is independent. success is defined as finding gold. the probability is the same for each trial.

julie created an app. she noticed that 10% of the users who downloaded her app upgraded within a week. let x be the number of customers who downloaded the app within a week. assuming the probability that each user's upgrades are independent, what type of variable is x?

geometric

lesson 20

geometric models for experimental studies in social sciences

what is the probability model of the people surveyed?

gym only : 18% park only : 23% swimming pool only : 10% community center : 49%

based on the data in the table, which map has the highest probability of getting him to his location in kenya?

map 4

what is the probability that 2 out of 5 investment bankers went to a top tier college?

p(x = 2) = 0.1382

lesson 17

permutations in social science experiments and studies

which scenarios involve permutations? select all that apply.

selecting a license plate with 2 letters and 3 numerals selecting a president and a vice president from among 10 senior staff members

two social workers conducted an experiment with a group of their patients. the study asked the patients a yes or no question. for the experiment to be considered a binomial model, what must be present? select all that apply.

the number of trials are fixed the outcome is only success or failure. each trial is independent but uses identical conditions.

how does the theoretical probability the spinner lands on a number less than 8 compare to the empirical probability of that happening?

the theoretical probability and the empirical probability are equal in value.

olive rolled a 6-sided number cube. what is the probability that the die will land on 2 or 3?

0.33

brenda tosses 2 number cubes with sides numbered from 1 to 6. what is the probability that the sum of the numbers is 5?

1/9

to reach a particular department at a warehouse, a caller must dial a 4-digit extension. suppose a caller remembers that the first and last digits of an extension are 5, but they are not sure about the other digits. how many possible extensions might they have to try?

100

in an election, there are 10 candidates in the first debate round. the 3 candidates receiving the most votes advance to the second debate round. how many different groups could participate in the second debate round?

120

a researcher is conducting an experiment to test a new vitamin supplement. the researcher has recruited 8 participants and must divide them into two groups of 4 people each. one group will receive the supplement, while the other group will receive a placebo pill. how many ways can the researcher create the two groups for the experiment?

140

a company requires a password to access a data storage vault. the password must be 4 characters long and may contain digits and lowercase letters only. how many passwords are possible if characters can be repeated?

1679616

a school committee voted to elect a member to be president and a member to be secretary. there are 15 members on the committee. how many different ways can they choose a president and secretary?

210

what is the empirical probability that teacher #4 will tutor students after school?

23%

a pregnant woman learns she is having twins. assuming the probability of having a girl and a boy are the same, what is the probability that the twins are two girls?

25%

a research group recruits 10 volunteers to try a new brand of tennis shoes. only 5 volunteers will be selected to participate in the study. how many ways can the research group select 5 participants?

252

jacky hires 5 out of 10 people to build a garden. how many possible combinations of workers could she choose?

252

what is the binomial coefficient of this study?

28

based on the data table, what is the empirical probability of the archaeologist finding fossilized bones?

28.6%

a bank assigns a personal code to each of its customers. this bank currently has 1,207,354 customers. the personal code uses 2 distinct letters from 24 letters (all the letters in the alphabet expect o and i), followed by n distinct numerals from 0 to 9. what is the smallest value of n such that each customer gets a unique code?

4

a number of children are posing for a group picture. there are five 8-year-olds and four 9-year-olds posing in the picture. how many arrangements are possible where the 8-year-olds and 9-year-olds alternate in the lineup?

5! * 4!

mark has just became a historian at one of the national museums in new york. out of curiosity, he partnered with 5 other museum employees at 5 other museums and conducted research to find out how many men versus women visited the museums last month. what is the probability that a visitor, chosen at random, is a man who visited museum 3?

6.25%

members of a hospital advisory committee will be selected from 5 doctors and 4 nurses. the committee must have 2 doctors and 2 nurses. how many possible combinations of doctors and nurses could be chosen for the committee?

60

janet wants to purchase a new car. at the car dealership, a salesperson tells her she can choose from 10 car models, 7 exterior colors, and 9 interior colors. how many ways can janet customize a car?

630

in psychologist theory, there are 6 types of basic instincts in a human being, and personality is determined by the presence or absence (2 choices) of these 6 basic instincts. how many different types of personalities can be identified?

64

mr. hammond's art class consists of 5 sophomores, 4 juniors, and 9 seniors. they randomly select one student from each class session to select the music played during the class. the grade of the student that was picked for the first 8 class sessions is shown in the table. which statement is true about the theoretical and empirical probability of selecting a sophomore?

the theoretical probability is greater than the empirical probability.

lesson 18

theoretical and empirical probability in the social sciences

what is the theoretical and empirical probability of the town electing a female mayor?

theoretical probability is 44.44%; empirical probability is 44%.

how does the theoretical probability compare to the empirical results of tom's election?

tom's expected percentage : 11.1% tom's actual percentage : 16.1%