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

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

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

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

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

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

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

Multiplying and Adding B 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

Multiplying and Adding B 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

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)

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)

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.

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.

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?

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?

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)

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)

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.

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.

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?

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?

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?

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?

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.

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.