(In)dependent Events, Mutually Exclusive Events, Combinations, Permutations

First Comb./Perm.

1

What do we type in Desmos to calculate combinations?

nCr

2

What does "n" refer to? 

The total number of possible choices. 

3

You can customize a burger with 5 toppings. You get to choose from 13 toppings. How many ways can you customize this burger?

nCr (13,5) = 1287

4

There are 20 math teachers at ACHS. How many ways can we select 4 of them to teach AFDA!

nCr (20,4) = 4845

5

There are two columns in this review labeled "Comb./Perm.". How many ways can we select one review question from these columns?

nPr (10,1)  = 10

Mutually Exclusive Events

1

Name the only operation (+ - xx-:) that is used in mutually exclusive events? 

Addition

2

What is this symbol?

 

Union

Or

We add probabilities when we see this symbol

3

You have 18 fish in a fish tank. 8 are solid colored, 4 are spotted, and 6 are striped.

What is the toal probability that you select a solid fish or a striped fish?  

P(solid OR striped) = 8/18 + 6/18 = 14/18

14/18 = 7/9

Mutually Exclusive Event

4

On a number wheel with numbers from 1-10, what's the probability of randomly selecting a odd number or a number less than 8?

P(odd OR <8) = 5/10 + 7/10 = 12/10

Non-Mutually Exclusive Event

5

You are driving and come to a 4 way stop. What is the probability that you turn right or left?

1/3+1/3=2/3

We can turn left, right, or go straight for a total of 3 options. 

Mutually Exclusive

Dependent vs. Independent Events

1

A bag contains 5 red marbles and 3 blue marbles. You select a red marble then replace it. What is the probability of drawing a blue marble on the second selection?

P(blue marble) = 3/8

Independent Event

2

A bag contains 5 red marbles and 3 blue marbles. You select a red marble and place it on the table. What is the probability of drawing a blue marble on the second selection?

P(blue marble) = 3/7

Dependent Event

3

A coin is tossed 17 times. What is the probability of getting heads on the 15th toss?

P(heads) = 1/2

Independent Event

4

When you leave this class, you make a right. When I leave this class, I also turn right. 

What is the probability that I turn right even though you already turned right? 

P(I turn right) = 1/2

Independent Event

5

You take a blue ball from the jar. You take a pink ball from the jar. 

P(blue) = 1/5

P(pink) = 1/4 

Dependent Event. 

Second Comb./Perm.

1

What do we type in Desmos to calculate permutations?

nPr

2

What does "r" refer to? 

The total number of choices that are used/chosen. 

3

How many ways can 10 students fill the student government positions of president, vice president, secretary, and treasurer?

5040

4

You have 6 places at King Street to eat lunch in the cafeteria. You're sneaky and found a way to eat lunch at 2 different places during your lunch block. How many ways can you select 2 places to eat lunch? 

nCr (6,2) = 15

5

You forgot the Probability Test is the next class! It covers mutually exclusive events, dependent vs. independent events, permutations, and combinations. You only have time to study 2 sections of the unit. In your study session, how many ways can you study 2 sections.

nCr (4,2) = 6

Mixed Bag

1

Give me a good definition for mutually exclusive events.

When two events cannot happen simultaneously.

2

How can I differentiate between combinations and permutations?

Permutations - ORDER MATTERS

Combinations - Order does NOT matter

3

What is this? 

Permutation Lock

4

You have to read 3 chapters before your next Science class. One chapter has 13 pages, another chapter has 17 pages, and the other chapter has 12 pages. How many ways can you read ANY 2 of those chapters before your next English class? 

nCr (3,2) = 3

5

Take a shot for 5 points. No doubling.