Warm Up Tyler has a bucket of 30 blocks. There are 8 cubes, 6 cylinders, 12 prisms and 4 pyramids. 1) What is the theoretical probability (%) of drawing a cube out of the bucket? 2) If Tyler continues drawing blocks and putting them back in 40 times, and pulls a cube 12 times, what is the experimental probability (%)of pulling a cube? 3) Why are the probabilities (%) different?

P(rolling two 3’s) 1 2. P(total shown > 10) 36 1 12 An experiment consists of rolling two fair number cubes. Find each probability. P(rolling two 3’s) 2. P(total shown > 10) 1 36 1 12

Independent and Dependent Events Course 3 10-5 Independent and Dependent Events Learn to find the probabilities of independent and dependent events.

Insert Lesson Title Here Course 3 10-5 Independent and Dependent Events Insert Lesson Title Here Vocabulary compound events independent events dependent events

Independent and Dependent Events Course 3 10-5 Independent and Dependent Events A compound event is made up of one or more separate events. To find the probability of a compound event, you need to know if the events are independent or dependent. Events are independent events if the occurrence of one event does not affect the probability of the other. Events are dependent events if the occurrence of one does affect the probability of the other.

Independent and Dependent Events Course 3 10-5 Independent and Dependent Events Determine if the events are dependent or independent. (Hint: Does the first even have any effect on the second event?) A. getting tails on a coin toss and rolling a 6 on a number cube B. getting 2 red gumballs out of a gumball machine

Independent and Dependent Events Course 3 10-5 Independent and Dependent Events Determine if the events are dependent or independent. (Hint: Does the first even have any effect on the second event?) A. rolling a 6 two times in a row with the same number cube B. a computer randomly generating two of the same numbers in a row

Independent and Dependent Events Course 3 10-5 Independent and Dependent Events

What is the probability that when you roll the dice, and spin the spinner that you get a 3 on each?

If you roll the dice, what is the probability that you will get an even number on both dice?

Independent and Dependent Events Course 3 10-5 Independent and Dependent Events Three separate boxes each have one blue marble and one green marble. One marble is chosen from each box. What is the probability of choosing a blue marble from each box?

Independent and Dependent Events Course 3 10-5 Independent and Dependent Events Three separate boxes each have one blue marble and one green marble. One marble is chosen from each box. What is the probability of choosing a blue marble, then a green marble, and then a blue marble?

Independent and Dependent Events Course 3 10-5 Independent and Dependent Events One box contains 4 marbles: red, blue, green, and black. What is the probability of choosing a blue marble, replacing it, and pulling blue again?

Jared is going to perform an experiment in which he spins each spinner once. What is the probability that the first spinner will land on A, the second spinner will land on an even number, and the third spinner will land on Blue? Express your answer as a fraction in simplest form.

Jean spins two spinners. Find the probability that the first spinner will NOT show an even number and that the second spinner will NOT show an odd number. Express your answer as a fraction in simplest form.

Independent and Dependent Events Course 3 10-5 Independent and Dependent Events One box contains 4 marbles: red, blue, green, and black. What is the probability of choosing a blue marble, not replacing it and then pulling a red? How is this problem different from the others? How do you think this will change the way we work the problem?

Independent and Dependent Events Course 3 10-5 Independent and Dependent Events To calculate the probability of two dependent events occurring, do the following: 1. Calculate the probability of the first event. 2. Calculate the probability that the second event would occur if the first event had already occurred. 3. Multiply the probabilities.

Independent and Dependent Events Course 3 10-5 Independent and Dependent Events The letters in the word dependent are placed in a box. If two letters are chosen at random, what is the probability that they will both be consonants? (Without replacement)

Independent and Dependent Events Course 3 10-5 Independent and Dependent Events The letters in the word dependent are placed in a box. If two letters are chosen at random, what is the probability that they will both be both be vowels? (Without replacement)

Independent and Dependent Events Course 3 10-5 Independent and Dependent Events Two mutually exclusive events cannot both happen at the same time. Remember!

Independent and Dependent Events Course 3 10-5 Independent and Dependent Events The letters in the phrase I Love Math are placed in a box. If two letters are chosen at random, what is the probability that they will both be consonants? (Without replacement)

Independent and Dependent Events Course 3 10-5 Independent and Dependent Events The letters in the phrase I Love Math are placed in a box. If two letters are chosen at random, what is the probability that they will both be vowels? (Without replacement)

Independent and Dependent Events Insert Lesson Title Here Course 3 10-5 Independent and Dependent Events Insert Lesson Title Here Lesson Quiz Determine if each event is dependent or independent. 1. drawing a red ball from a bucket and then drawing a green ball without replacing the first 2. spinning a 7 on a spinner three times in a row 3. A bucket contains 5 yellow and 7 red balls. If 2 balls are selected randomly without replacement, what is the probability that they will both be yellow? dependent independent 5 33

WARM UP The Venn diagram below shows how many of the 500 students at Hayes Middle school watched only the Olympics, watched only the All-Star Basketball game, or watched both events. What is the probability that a student randomly selected while walking in the hall watched the Olympics that weekend? Justify your solution.

What is the probability that a student randomly selected while walking in the hall watched the All-Star Basketball game that weekend? Justify your solution. the hall watched neither the Olympics nor the All-Star Basketball game that weekend? Justify your solution.

A fair number cube and a coin are used to collect data. The faces of the cube are colored: red, green, blue, orange, yellow, and purple. What is the probability of rolling a green or a yellow, and then flipping the coin and getting heads?

Joe has 11 markers in a backpack. One of them is dark brown and one is tan. Find the probability that Joe will reach into the backpack without looking and grab the dark brown marker and then reach in a second time and grab the tan marker. Express your answer as a fraction in simplest form.

Jake the magician has the following items in his hat: 1 scarf, 2 rabbits, 2 doves, and 2 bouquets of flowers. The magician draws 1 item and does not replace it before drawing a second item. What is the probability of the magician drawing a rabbit and then a dove out of his hat?

Sarah is playing a game with 3 six-sided number cubes. Each cube is numbered 1 through 6. If Sarah rolls 3 ones, she will lose all of her points. What is the probability that she will roll 3 ones?

Jordan wants the probability of drawing a blue tile and then drawing a second blue tile to be 1/28, if the first blue tile is not replaced. If there will only be 2 blue tiles in the bag, how many total tiles should be placed in the bag?

The 6 cards below were placed in a bag. A card is randomly drawn from the bag and not replaced. What is the probability of drawing an “O” card and then drawing another “O” card?

Derek placed 2 red tiles, 10 blue tiles, 5 green tiles, and 3 yellow tiles in a bag. He challenged his friends to draw randomly the 2 red tiles from the bag. Susan accepted the challenge. She drew one tile, did not replace it, and drew a second tile. What is the probability that Susan will draw 2 red tiles?

You have a bag that contains 7 candies: 3 mints, 2 butterscotch drops, and 2 caramels, with the candies thoroughly mixed. • Which of the following statements are true? • Which are not true? • Justify your solutions.