1. Probability Practice Problems
After sitting through the twenty-third example about playing cards in his probability class, the student raised his hand to complain:
"Professor, all this talk makes me feel like I'm turning into a deck of cards."
The professor turned to the student and replied, "Be patient and I'll deal with you later."
Alg 2/Trig Honors

2. Geometric Probability
A dart is thrown at random at the target shown. What is the probability the dart lands in the shaded region?
△ABC is an equilateral triangle 12

3. Geometric Probability
A dart is thrown at random at the target shown. What is the probability the dart lands in the shaded region?
△ABC is an equilateral triangle 12

4. Mutually Exclusive
Consider rolling a pair of fair, 6-sided dice. Event A is that the sum of the dice is 10. a. Give an example of Event B such that Events A and B are mutually exclusive. b. Give an example of Event B such that P(A and B) = 1 36

5. Mutually Exclusive
Consider rolling a pair of fair, 6-sided dice. Event A is that the sum of the dice is 10. a. Give an example of Event B such that Events A and B are mutually exclusive. b. Give an example of Event B such that P(A and B) = 1 36

6. Pick a card, any card!
A card is selected at random from a standard, 52-card deck. Find the following probabilities: a. Selecting a two b. Selecting a two or three c. Selecting a four, five, or spade d. Selecting a red or queen e. Selecting a black heart

7. Pick a card, any card!
A card is selected at random from a standard, 52-card deck. Find the following probabilities: a. Selecting a two b. Selecting a two or three c. Selecting a four, five, or spade d. Selecting a red or queen e. Selecting a black heart

8. Multiplying and AddingB A C
A four-sided die with letters, A, B, C, and D is rolled.
What is the probability that A is rolled:
On all four rolls b. At least one time
c. On exactly one roll d On at least two rolls? D

9. Multiplying and AddingB A C
A four-sided die with letters, A, B, C, and D is rolled.
What is the probability that A is rolled:
On all four rolls b. At least one time
c. On exactly one roll d On at least two rolls? D

10. Dependent Events
A bag of troll dolls includes 4 red dolls, 5 blue dolls, and 1 yellow doll. Two dolls are selected from the bag, without replacement. Find each of the following probabilities: P(selecting a red doll, then a blue doll) P(selecting two red dolls) P(selecting at least one red doll) P(selecting two yellow dolls)

11. Dependent Events
A bag of troll dolls includes 4 red dolls, 5 blue dolls, and 1 yellow doll. Two dolls are selected from the bag, without replacement. Find each of the following probabilities: P(selecting a red doll, then a blue doll) P(selecting two red dolls) P(selecting at least one red doll) P(selecting two yellow dolls)

12. Independent Events – Apps of Mult/Add
A coin is flipped 4 times. a. List the sample space b. Draw a probability distribution c. What is the probability that the coin lands on Heads exactly twice? d. What is the probability the coin lands on Heads more than twice.

13. Independent Events – Apps of Mult/Add
A coin is flipped 4 times. a. List the sample space b. Draw a probability distribution c. What is the probability that the coin lands on Heads exactly twice? d. What is the probability the coin lands on Heads more than twice.

14. Independent Events – Apps of Mult/Add
 A six-sided die is rolled until a 1 or 2 comes up. What is the probability this occurs on the third roll?

15. Independent Events – Apps of Mult/Add
 A six-sided die is rolled until a 1 or 2 comes up. What is the probability this occurs on the third roll?

16. Conditional Probability - Tables
The table below illustrates sales figures from a local car dealership for March, 2017.
Sedan
SUV
New 14 9
Used 11 21
A car is selected at random. Determine the following probabilities: a. P(New) b. P (New | SUV) c. P (SUV | New) d. P (Used Sedan) e. P(Used or Sedan)

17. Conditional Probability - Tables
The table below illustrates sales figures from a local car dealership for March, 2017.
Sedan
SUV
New 14 9
Used 11 21
A car is selected at random. Determine the following probabilities: a. P(New) b. P (New | SUV) c. P (SUV | New) d. P (Used Sedan) e. P(Used or Sedan)

18. Conditional Probability – Tree Diagram
At a local restaurant, customers can either dine-in or take the food to-go. Typically, 80% of customers dine-in, and 42% of the dine-in customers order dessert. Alternatively, only 15% of to-go orders include dessert. If an order includes dessert, find the probability it was from a take-out order. Find the probability that an order is to-go and does not include dessert.

19. Conditional Probability – Tree Diagram
At a local restaurant, customers can either dine-in or take the food to-go. Typically, 80% of customers dine-in, and 42% of the dine-in customers order dessert. Alternatively, only 15% of to-go orders include dessert. If an order includes dessert, find the probability it was from a take-out order. Find the probability that an order is to-go and does not include dessert.

20. Conditional Probability – Challenge Level 1
David has a bag containing six fair coins and four double-headed coins. He takes a coin at random from the bag and tosses it in the air.
Given the outcome was heads, what is the probability that David picked a double-headed coin?

21. Conditional Probability – Challenge Level 1
David has a bag containing six fair coins and four double-headed coins. He takes a coin at random from the bag and tosses it in the air.
Given the outcome was heads, what is the probability that David picked a double-headed coin?

22. Conditional Probability – Challenge Level 2
Team North is competing against Team South in a competition. Team North has an 80% probability of knowing how to do a problem, and a 90% probability of getting the right answer when they know how to do a problem. Team South has a 95% probability of knowing how to do a problem, and a 75% probability of getting the right answer when they know how to do a problem. What is the probability that Team North answers a question correctly and Team South gets it wrong?

23. Conditional Probability – Challenge Level 2
Team North is competing against Team South in a competition. Team North has an 80% probability of knowing how to do a problem, and a 90% probability of getting the right answer when they know how to do a problem. Team South has a 95% probability of knowing how to do a problem, and a 75% probability of getting the right answer when they know how to do a problem. What is the probability that Team North answers a question correctly and Team South gets it wrong?

24. Conditional Probability – Challenge Level 3
Box A contains 4 red and 2 green marbles. Box B contains 1 red and 3 green marbles. Box C has 3 red marbles and 4 green marbles. One marble is randomly chosen from each of Box A and Box B. These two marbles are put into Box C. Then, one marble is randomly chosen from Box C.
Find the probability that this marble is red.

25. Conditional Probability – Challenge Level 3
Box A contains 4 red and 2 green marbles. Box B contains 1 red and 3 green marbles. Box C has 3 red marbles and 4 green marbles. One marble is randomly chosen from each of Box A and Box B. These two marbles are put into Box C. Then, one marble is randomly chosen from Box C.
Find the probability that this marble is red.