Instructions: In each group, please come up with a - - PowerPoint PPT Presentation

Instructions: In each group, please come up with a scenario/experiment for each of the three main kinds of probability problems we have talked about: With replacement, Without replacement (and order matters), Without replacement (and order doesn’t matter). Write your experiments/scenarios below (so that we can share them with the other groups!) and for each one, please write a sentence or two about how you know that scenario is the particular kind you said. For example, if your experiment was “Rolling 4 dice”, you might say “This is a “with replacement” problem because the numbers on the dice can repeat. If you get a 5 on the first roll, it is still possible to get a 5 on the second roll. Clarification: For each scenario, please include a probability problem, not just the “set-up”. For example, instead of just writing “Rolling dice” or “Rolling 4 dice”, I’m looking for the full problem, so “Roll 4 dice and what is the probability that you get all heads” or something like that. So like,

• ne “part” from a usual homework problem!

New instruction! After you’ve come up with all of your problems, please pick one and try to solve it! (You don’t have to write the solution on the google doc, just practice solving it in your group.) After that, if you still have time left, you can try solving another one! Group 1: Replacement (order matters): Tiger Woods is playing a round of golf. He can score under par (0.45), at par (0.40), or over par (0.15). What is the probability that he scores at par for the first three holes? No replacement (order matters): Organizing library books in alphabetical order. A library has 6

• books. Half the books fall off the shelf. What is the probability the 3 books that fell have titles

that start with the letters A-F? Assuming all the letters have the same probability. No replacement (order doesn’t matter): Select 4 kids for a group in a class of 28 kids (15 boys, 13 girls) to create 7 groups. What is the probability that a group will have two boys and two girls? Group 2: Without replacement (order doesn’t matter):

This is without replacement and order doesn’t matter because you can pick the puppies in either

• rder and it doesn’t change the probability of getting both together.

Without replacement and order matters: ​There are ten students in the class. 6 are

• female. 4 are male. There are three positions in student government - President, VP,
• Secretary. What is the probability that I select a Female President, a Male VP and a

Female Secretary? Here order matters because changing the order would change the outcome. With replacement:​ In a bag with 9 marbles, 3 are blue, 3 red, and 3 are green. What is the probability that the first is red and the third is green? You are replacing the marbles each time. Group 3: With replacement: (There is a daily lottery and the six numbers that are picked are 5,10,15,20,25,30. What is the probability that the lottery ticket for Monday will have one the same number as Sunday ticket?

• This is with replacement because the next day is a completely new game - you start all over

again.) There is a volleyball league. There are 10 teams that compete. The Green Team won the championship last year. They won 60% of their games. What is the probability that the Green team wins the first three games in a row? Without replacement (order matters): In a spelling bee, there is a first place, second place, and third place winner. There are seven kids in the final. Four are girls, three are boys. What is the probability that all three will be girls?

• This is without replacement because one person can’t win both first and second place. Order

matters because if Grace wins first and Anna wins second, that is a different outcome than if Anna wins first and Grace wins second. Without replacement (order doesn’t matter): You are ordering ice cream at Baskin-Robbins and there are 31 flavors and seven different ice cream toppings. You can pick one flavor and one topping. What’s the probability that they pick chocolate with sprinkles?

• Group 4:

Replacement​: If there are 5 breakout groups each week during our zoom session, what is the probability that you will be in group 2 each time during the first 3 weeks? We know this is replacement, we are put back into the general pool of students each time. No Replacement, Order Matters: ​There are 21 students in the class, 11 boys and 10 girls, and we choose students for 5 classroom jobs(line leader, board cleaner, runner, pencil sharpener, librarian). What is the probability that the line leader and the runner are a girl? We know this is no replacement, order matters because once a student is chosen they don’t go back into the pool of students and the order matters because they can’t have more than one role. So if student A is chosen for line leader, they can’t be any other job. Total Outcomes: 21P5=21*20*19*18*17=2,441,880 E: Line leader and runner are a girl E: 10*9*19*18*17=523,260 P(E)=523,260/2,441,880=approx 21% No Replacement, Order Doesn’t Matters​: If you draw 2 cards in a game of blackjack using a standard 52 card deck, what is the probability that the 2 cards drawn add up to 21? We know no replacement because the cards don’t go back into the original deck and they go to a discard

• pile. We know this order doesn’t matter because drawing a ace and ten or drawing a ten and

ace both equal 21. Total Outcomes: 52C2: (52*51)/2*1=1326 E: Choosing 2 cards that equal 21 E: 4C1*16C1=64 P(E)=64/1326=approx 4.8% (1 in 21! 😴) Group 5: 1.) Replacement :

You are playing the game of life and are using the spinner (1 to 10) to determine how many moves you could make. What is the probability that you will spin greater than 5 three times in a row? (12.5%)

• This is a replacement problem because if you spin a number it does not get taken
• ff.

2.) Without Replacement-Order Matters- In gym class choosing teams for soccer, 1st person is captain, second person is goalie, third is center, and fourth is defense. If you have 13 kids ( 8 tall and 5 short), What is the probability that the captain is tall and the goalie is short? (27%)

• Once a kid has a position they cannot be assigned a position, and we said that
• rder pick assigns roles.

3.) Without Replacement- Order Doesn't Matter- You are at Mariano's salad bar and want to get lunch for your family. You are going to choose 5 different foods to put in the salad. The salad bar has 4 proteins, 4 vegetables, 2 greens, and 3 dressings. What is the probability that your salad has at least 2 vegetables?

• This is a without replacement problem because you wouldn’t take two servings of

the same thing. The order doesn’t matter because salad is just going to get mixed up before it gets eaten.