Tables and Diagrams
In a survey of 100 people, 45 like dogs, 35 like cats, and 15 like both. How many people like only dogs?
30 people
A jar contains 5 red, 8 blue, and 7 green marbles. What is the probability of randomly drawing a red marble?
5/20 = 1/4
Are drawing a card from a deck, replacing it, and then drawing another card considered independent or dependent events?
Independent
True or False: Two events are mutually exclusive if they can both happen at the same time.
False
What are complementary events?
Events that are opposites but contain ALL possible outcomes and sum to 1.
A two-way table shows 50 students were surveyed about their favorite class (math or English) and whether they prefer morning or afternoon. 20 students prefer math and morning, 15 prefer math and afternoon. 10 students prefer English and morning, and 5 prefer English and afternoon. What is the probability that a randomly selected student prefers math?
35/50 = 7/10
A jar contains 5 red, 8 blue, and 7 green marbles. What is the probability of drawing a blue marble, not replacing it, and then drawing a red marble?
2/19
A bag contains 4 red and 6 blue marbles. Are drawing a red marble and then drawing a second red marble without replacement independent or dependent events?
Dependent
Are the events "rolling a 3 on a six-sided die" and "rolling an even number on the same die" mutually exclusive or inclusive?
Mutually exclusive
A bag contains 10 green marbles, 8 yellow marbles, and 2 orange marbles. What is the probability of drawing a yellow or an orange marble?
10/20 = 1/2
A Venn diagram for a group of 160 people shows that 80 like comedy movies, 60 like action movies, and 20 like both. How many people like neither comedy nor action movies?
40 people
In a bag of candy, there are 10 pieces of chocolate, 8 pieces of taffy, and 7 pieces of caramel. You reach in and pull out two pieces of candy without replacement. What is the probability that you pull out a caramel piece first, followed by a piece of chocolate?
7/60
If two events, A and B, are independent, what is the formula for calculating P(A and B)?
P(A) x P(B)
Are the events "drawing a red card" and "drawing a King" from a standard deck of cards mutually exclusive or inclusive?
Mutually inclusive
You have a bag with 10 marbles: 4 are red, 6 are blue. What is the probability of drawing a blue marble, then a red marble, without replacement?
4/15
Based on a survey of 200 students, create a Venn diagram showing the relationship between having a smartphone and having a laptop. We know 120 students have a smartphone, 80 students have a laptop, and 50 students have both. What is the probability that a student has a smartphone but no laptop?
70/200 = 7/20
A standard 52-card deck is used. Given that you drew a red card, what is the probability that the card was an ace?
2/26 = 1/13
A coin is flipped, and a six-sided die is rolled. What is the probability of rolling a 5 AND getting heads?
1/2(1/6) = 1/12
A survey shows that in a group of 50 students, 20 play the guitar and 15 play the piano. 5 students play both. Based on this, are the events "playing the guitar" and "playing the piano" mutually exclusive or inclusive?
Mutually inclusive
A survey of 200 people shows that 120 people own a car, and 90 people own a bike. 60 people own both a car and a bike. What is the probability that a randomly selected person owns a car, given that they own a bike?
2/3
A two-way table shows 50 students were surveyed about their favorite class (math or English) and whether they prefer morning or afternoon. 20 students prefer math and morning, 15 prefer math and afternoon. 10 students prefer English and morning, and 5 prefer English and afternoon. What is the probability that a randomly selected English lover prefers the afternoon?
5/15 = 1/3
In a class of 30 students, 12 play basketball and 8 play tennis. 3 students play both. What is the probability that a student plays basketball, given that they also play tennis?
3/8
A bag contains 8 red, 6 blue, and 6 green marbles. You randomly draw one marble, then a second, and finally a third, without replacement. What is the probability that you draw a red marble, then a blue marble, then a green marble?
4/95
In a group of 50 students, 18 play soccer, 22 play basketball, and 12 play neither. What is the probability that a randomly selected student plays soccer or basketball?
38/50 = 19/25
A group of 200 students were surveyed. The probability of a student being in the band is 1/4. The probability of a student being on the football team is 1/5. Ten students are on both teams. How MANY students are in band OR on the football team?
80 students