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Tyler has a bucket of 30 blocks. There are8 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 cube12 times, what is the experimental probability (%)of pulling a cube?
3) Why are the probabilities (%) different?
An experiment consists of rolling two fair number cubes. Find each probability.
1. P(rolling two 3’s)
2. P(total shown > 10)
136
112
Learn to find the probabilities of independent and dependent events.
Course 3
10-5 Independent and Dependent Events
Vocabulary
compound events
independent eventsdependent events
Insert Lesson Title Here
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.
Course 3
10-5 Independent and Dependent Events
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.
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
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
Course 3
10-5 Independent and Dependent Events
Course 3
10-5 Independent and Dependent Events
Probability with Replacement
I have four coins in my purse: a penny, a nickel, a dime and a quarter.
If I have all four coins in my coin purse, what is the probability that I will pull out a quarter?
If I put the quarter back in my purse, what is the probability that I will pull out a nickel?
Probability without Replacement
I have four coins in my purse: a penny, a nickel, a dime and a quarter.
If I have all four coins in my coin purse, what is the probability that I will pull out a quarter?
If I leave the quarter out of my coin purse, what is the probability that I pull out a dime?
What is the probability that when youroll the dice, and spin the spinnerthat you get a 3 on each?
If you roll the dice, what is the probability thatyou will get an even number on both dice?
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?
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?
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?
Course 3
10-5 Independent and Dependent Events
A
B
Spinner 1
1
2
3
4
Spinner 2
Red
Green
Blue
Spinner 3
Jared is going to perform an experiment in which hespins 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.
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?
Course 3
10-5 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.
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)
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)
Course 3
10-5 Independent and Dependent Events
Course 3
10-5 Independent and Dependent Events
Two mutually exclusive events cannot both happen at the same time.
Remember!
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)
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)
Course 3
10-5 Independent and Dependent Events
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?
independent
dependent
Insert Lesson Title Here
533
Course 3
10-5 Independent and Dependent Events
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 inthe hall watched the Olympics that weekend? Justify your solution.
WARM UPWARM UP
What is the probability that a student randomly selected while walking inthe hall watched the All-Star Basketball game that weekend? Justify yoursolution.
What is the probability that a student randomly selected while walking inthe hall watched neither the Olympics nor the All-Star Basketball gamethat weekend? Justify your solution.
A fair number cube and a coin areused to collect data. The faces of thecube are colored: red, green, blue,orange, yellow, and purple. What isthe probability of rolling a green ora yellow, and then flipping the coinand getting heads?
Joe has 11 markers in a backpack. One of them is darkbrown and one is tan. Find the probability that Joe willreach 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 followingitems in his hat: 1 scarf, 2 rabbits,2 doves, and 2 bouquets of flowers.The magician draws 1 item anddoes not replace it before drawing asecond item. What is the probabilityof the magician drawing a rabbitand then a dove out of his hat?
Sarah is playing a game with 3 six-sided number cubes. Each cube isnumbered 1 through 6. If Sarah rolls3 ones, she will lose all of herpoints. What is the probability thatshe will roll 3 ones?
Jordan wants the probability ofdrawing 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 be2 blue tiles in the bag, how manytotal tiles should be placed in thebag?
The 6 cards below were placed in a bag.
A card is randomly drawn from thebag and not replaced. What is theprobability of drawing an “O” cardand then drawing another “O” card?
Derek placed 2 red tiles, 10 bluetiles, 5 green tiles, and 3 yellow tilesin a bag. He challenged his friendsto draw randomly the 2 red tilesfrom the bag. Susan accepted thechallenge. She drew one tile, did notreplace it, and drew a second tile.What is the probability that Susanwill 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.
