1.3 Counting

Question 1

The Probability of the Interserction of Independant Events

Answer 1

P(AnBnCn..Z)= P(A)P(B)P(C)*P(Z)

Whenever more than one indep events occurs, multiply their probabilities together

Question 2

When to use rule 1

Answer 2

• 0.57 like this 0.43 hate that; randomly chosen 2, prob of both liking?

-quiz has 4 questions with 4 answers each, randomly answer, prob of all correct?

Question 3

KEYWORD FOR RULE #1

Answer 3

RANDOMLY CHOSEN- means that A does not effect likeliness of B!

Question 4

Multiplicative rule

Answer 4

basically used when need to find the number of ELEMENTS in the intersection of independant events!!!!!!!!!!!!!!!

Question 5

Permutations

Answer 5

Order matters!

Pick
Arrange
One by one w/o replacements
Order

Question 6

Combinations

Answer 6

Order doesnt amtter

Select

Question 7

What is counting

Answer 7

Determingi elements in sample space

Question 8

Steps to counting

Answer 8

1. Figure out n(S) either with r^m or using nCr
2. For n(A) break up itno simpler concepts (is there any laws we can use?)
3. KEYWORDS?
   -Randomly chosen: independant
   -> or < use Box
   -Select use Circle!
   - Think is this ordered? If need be add an ordered combination

Question 9

How to add order to combinations

HOW TO CHECK

Answer 9

nCr

n= total amount in group
r= how many objects do we want?

4 EVEN CARDS PICK 2 (4C2)

Basically it gives us all possible outcomes of this scenario

CHECK BY WRITING OUT POSSIBILITIES!!!

Question 10

AIf a car is permanently chosen?

Answer 10

(1C1) like a king of diamonds

Question 11

Draw a diagram for?

Answer 11

All dice and card questions

Question 12

Perms can be written as?

Answer 12

COMBINATIONS

6X5X4
(6 1) (5 1) (4 1)

Question 13

How to do pair questions?

Answer 13

Make a pattern to visualize
AABCD

Question 14

SCENARIO

If all spots are the same?

Answer 14

Pick a leader!

Question 15

SCENARIO

Two diff event types? Independant from one another?

Answer 15

Use the circle split in half, use the RULE #1

Question 16

SCENARIO

AT least two are the same?

Answer 16

1-P(ALl different)

Question 17

SCENARIO

P(A pair)

Answer 17

AABCD

Write out a pattern

-Choose from both dimensions!! first faces, then from the objects, then faces left over, then objects left over

Question 18

SCENARIO

P two pairs

Answer 18

PATTERN AABCD

Choose from both dimensions!!!! First choose 2 from all faces, then 2 combs for each pair. then pick from left over faces, then comb for each left over object

Question 19

When order matters..

Answer 19

INCLUDE A COMB FOR IT!!!

Question 20

Can YOU POCK FOR TRIPLE AND PAIR AT ONCE?

Answer 20

NO ONLY FOR PAIR AND PAIR OR SINGLES!!!

NOT FOR A PAIR AND A TRIPLE