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Define when events are mututally exclusive.
They CANNOT happen at the same time.
Are the following events independent or dependent?
Event A: Drawing a heart from a deck of cards.
(not putting it back)
Event B: Drawing a queen.
Dependent
What does the following mean in words:
P(9th grader | plays a sport)
The probability that a student is in the 9th grade GIVEN they play a sport.
A local ice cream shop allows you to build your own sundae. You must choose exactly one from each of the following categories:
4 flavors of ice cream (Vanilla, Chocolate, Strawberry, Mint)
3 types of syrup (Fudge, Caramel, Strawberry)
5 different toppings (Sprinkles, Nuts, Cherries, Oreos, Gummy Bears)
How many different combinations are possible?
60
At a booth, you pay $5 to play a game. There is a bag with 100 marbles:
1 gold marble wins $100
5 silver marbles win $20
94 black marbles win nothing
What is the expected value of a single play?
-$3.00
A single card is drawn from a standard deck of 52 cards. What is the probability that the card is either a King or a Heart?
16/52
You flip a fair coin twice. What is the probability that it lands on Heads both times?
1/4 or 0.25
What is the probability that a patient recovered given they wern to clinic B.
80/150
A teacher needs to select a leadership team from a class of 25 students. She needs to pick:
1 President
1 Vice President
1 Secretary
How many different ways can these positions be filled?
13,800
An investor is considering putting money into a tech startup. There is a:
10% chance the company goes public and the investor gains $500,000
30% chance it is acquired and the investor gains $100,000
60% chance the company fails and the investor loses $150,000
What is the expected profit or loss for this investment?
-$10,000
A fair six-sided die is rolled once. What is the probability of rolling a 2 or a 5?
2/6
A drawer contains 6 black socks and 4 blue socks. You reach in and grab two socks, one after the other, without replacing the first one. What is the probability that both socks are black?
30/90 or 1/3
What is the probability that the student did NOT recover given they went to clinic A.
30/150
North Carolina is designing a new licence plate that will be 4 letters followed by 2 digits (0-9). How many different licence plates are possible?
45,697,600
At a school fundraiser, you are invited to play a game using a spinner divided into three unequal sections:
Red (50%): You win $4
Blue (33%): You win $6
Green (17%): You win $12
The organizer wants to ensure the game is perfectly fair.
What should the price be to play?
$6.02
In a class of 30 students, 15 students play soccer, 10 students play basketball, and 4 students play both. If a student is chosen at random, what is the probability they play soccer or basketball?
21/30
What is the probability of rolling a 6 on a standard die and drawing an Ace from a standard deck of 52 cards?
1/78
What is the probability that a patient went to clinic A given they recovered.
120/200
The Junior Class needs to elect a leadership team from a pool of 10 qualified candidates. They need to fill three specific positions: President, Vice-President, and Treasurer.
How many different ways can these three positions be filled?
720
A player rolls a fair six-sided die.
If they roll a 6, they win $10.
If they roll a 5, they win $2.
If they roll any other number (1, 2, 3, or 4), they win nothing.
If it costs $3 to play, what is the expected value of this game?
-$1.00
A jar contains 5 red marbles, 8 blue marbles, and 7 green marbles. If you pick one marble at random, what is the probability it is red or green?
12/20
A system generates a 2-character security code. The first character must be a letter (A-Z) and the second must be a digit (0-9). What is the probability that a randomly generated code is "B7"?
1/260
What is the probability that a patient went to clinic B, given they did not recover?
70/100
A chemistry teacher needs to choose 3 students from a class of 10 to form a clean-up committee at the end of the lab period.
How many different ways can the teacher choose the group of 3 students?
120
A fisherman enters a contest where the prize is based on the weight of the largest fish caught:
20% chance of catching a "Trophy" fish: $500 prize
30% chance of catching a "Keeper" fish: $100 prize
50% chance of catching "Small" fish: $0 prize
If it costs $100 to enter, what is the expected winnings for a fisherman entering the contest?
$30