Basic Probability Concepts
Tables and Venn Diagrams
Sample Spaces
Compound Probability and Mutual Exclusivity
100
A spinner is divided into 12 equal sections. Four sections are blue, five are red, and three are green. What is the probability of spinning a color that is not red?
0.583 or 7/12
100
65 people were surveyed. What is the probability that a randomly selected person listens to music for less than 1 hour each day AND plays an instrument?
3/65
100
You flip a coin and roll a standard 6-sided die. How any total outcomes are in the sample space?
12
100
Jim rolls 3 dice. What is the probability they all show a number greater than 4?
8/216
200
A local raffle has a 15% win rate. If a school buys 400 tickets, how many winning tickets should they expect to have?
0.15(400)=60 wins
200
65 people were surveyed. What is the probability that a randomly selected person listens to music for more than 1 hour, each day?
51/65
200
You roll two dice and ADD the results. The sample space of possible outcomes is shown below. What are the least likely SUMS when rolling the dice?
2 and 12
200
An English class has a total of 25 students: 4 freshman, 9 sophomores, 7 juniors, and 5 seniors. Each week, two students are randomly chosen to lead a book discussion. Find the probability of two juniors being selected.
7/25*6/24=42/600
300
Using the word PROBABILITY, find the probability of randomly selecting a vowel or the letter B.
6/11
300
300 students were asked about the activities that they participate in after school. The results are shown in the Venn diagram below. How many students are involved in Drama OR Band, but NOT Football?
50+23+31=104 students
300
A coin is flipped and a spinner is spun. Find the probability of getting "not x" and "heads".
2/6
300
An English class has a total of 25 students: 4 freshman, 9 sophomores, 7 juniors, and 5 seniors. Each week, two students are randomly chosen to lead a book discussion. Find the probability of a freshman being selected, then anyone except a freshman being selected.
4/25*21/24=84/600
400
A gambler loses 10 times in a row at a slot machine with a 10% win rate and claims "they are due for a win" on the 11th try. Why is this reasoning mathematically incorrect?
Probability is unpredictable in the short term, and since the events are independent, the chance of winning remains 10% regardless of previous losses.
400
65 people were surveyed. What is the probability that a randomly selected person does not play an instrument OR listens to music for less than 1 hour daily?
36/65
400
You roll two dice and ADD the results. The sample space of possible outcomes is shown below. Find the probability of getting a SUM greater than 10.
3/36
400
A survey asks "Do you play the guitar or do you have a job?"
Are "playing the guitar" and "having a job" mutually exclusive? Explain.
No, they are not mutually exclusive. Someone can both play the guitar and have a job. Those traits do not exclude (stop) each other from happening.
500
A certain brand of flower, when planted, has an 82% germination (sprout) rate. Interpret the meaning of "82% probability" in the context of this situation.
If you plant many many of these flower seeds, then about 82% of them will germinate.
500
At a library, 100 guests were randomly asked about the books that they were checking out. 30 guests checked out a mystery novel, 22 guests checked out a romantic novel, and 5 guests checked out both.
Draw a Venn diagram. How many guests checked out neither a mystery nor romantic novel?
53 checked out neither
500
A survey asked people what their favorite ice cream flavor is. The results are shown. What percent of respondents said "none"?
8%
500
A baby has a 10% probability of being born prematurely.
If the baby is born prematurely, there is a 40% probability it will have breathing issues.
If the baby is not born prematurely, there is a 5% probability it will have breathing issues.
Draw a tree diagram for this situation. Find the probability that the baby will not have breathing issues.
