Combinations
A class has 5 boys and 3 girls. If a teacher wants to select one boy and one girl for a project, how many different ways can she make this selection?
15
A single die is rolled. What are the odds in favor of rolling a number greater than 4?
2:4 or 1:2
A school of 300 students is surveyed about their preferences:
Find P(Math)
150/300
A health researcher conducts a study where one group of participants is asked to follow a specific diet plan for 6 months, while a second group continues their normal eating habits. The researcher then compares the health outcomes of both groups.
Experimental study
The following table shows the favorite types of pets among a group of 100 students.
What fraction of the students prefer dogs?
40/100
How many different ways can you arrange the letters of the word "COMBINATORICS"
778,377,600
A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If a marble is selected at random, what are the odds against selecting a blue marble?
7:3
A school of 300 students is surveyed about their preferences:
Find P(NO)
130/300
A polling company conducts a survey of 1,000 people to estimate the average number of hours people in a city watch TV each week. The sample was randomly selected from a list of city residents by creating groups of 200 and then selecting 12 of 5 of the groups.
What type of sampling method was used?
The following table shows the favorite types of pets among a group of 100 students.
What percentage of students prefer cats?
30%
From a group of 10 people, how many different ways can a committee of 4 people be selected, without regard to the order of selection?
210
You flip a fair coin. If it lands heads, you win $4; if it lands tails, you lose $3. What is the expected value of this game?
$0.5
A school of 300 students is surveyed about their preferences:
Find P(Math or Science)
170/300
A survey is conducted in a city to determine residents' views on a new public transportation plan. The survey is conducted on a Saturday afternoon at a popular downtown shopping mall.
Exclusion bias
The following table shows the favorite types of pets among a group of 100 students.
What fraction of students prefer either birds or fish?
25/100
A password consists of 3 letters, followed by 3 digits. If repetition of letters and digits is allowed, how many different possible passwords can be formed?
17,576,000
Describe how to determine if a game is a fair game.
Expected value is 0
A school of 300 students is surveyed about their preferences:
Find P(Math and Science)
100/300
A survey is conducted in a city to determine residents' views on a new public transportation plan. The survey asked respondents what they liked most about the plan.
What type of bias could affect the results?
Response bias
The following table shows the favorite types of pets among a group of 100 students.
What is the ratio of students who prefer dogs to those who prefer other pets?
40:30
From a group consisting of 6 women and 4 men, a committee of four will be formed. How many committees can be formed if 2 women and 2 men are selected?
90
In a game of roulette, you place a $5 bet on a single number. If you win, you get $35. The probability of winning on a single number is 1/38, and the probability of losing is 37/38. What is the expected value?
-$4.08
A school of 300 students is surveyed about their preferences:
Find P(Math|Science)
100/120
A pollster wants to estimate the political preferences of a country's population. They randomly select 500 people by choosing names from a national voter registration list.
What type of sampling method was used?
Simple Random Sample
The following table shows the favorite types of pets among a group of 100 students.
If 10 more students are surveyed and they all prefer cats, how would this affect the percentage of students who prefer cats?
It would increase from 30% to 36%