naive definition of probability (week 1)

Question 1

sample space (S)

Answer 1

set of all possible outcomes

Question 2

intersect ?

Answer 2

n

Question 3

disjoint ?

Answer 3

AnC = no result

Question 4

Probability naive formula

Answer 4

num of elements in A / num of elements in sample space

Question 5

naive because

Answer 5

assume its finite

Question 6

P(AnB) formula

Answer 6

P(A)-P(B)

Question 7

P(AuB) formula

Answer 7

P(A)+P(B)-P(AnB)

Question 8

what is an event?

Answer 8

Subset of a sample

Question 9

union symbol?

Answer 9

u

Question 10

empty set symbol

Answer 10

∅

Question 11

A u A^c =

Answer 11

S

Question 12

A n A^c

Answer 12

∅

Question 13

mutually exclusive is when

Answer 13

the instersection is empty

Question 14

distributive rule

Answer 14

A n (B u C) = (A n B) u (A n C)

Question 15

De morgans law

Answer 15

(A n B) ^ c = A^c u B^c

Question 16

Cardinality is

Answer 16

denotes by |A| means the number of elements in A

Question 17

At least formula

Answer 17

– the complement

Question 18

permutations, order matter

Answer 18

pake !
misal, how many configurations of 13 hearts? 13!

Question 19

permutations, choose k times from n with replacement , order matters

Answer 19

n^k

Question 20

permutations, choose k from n, with NO replacement, order matters

Answer 20

nPk = n! / (n-k)!

Question 21

permutations choose k times from n, NO replacement, order does not matter

Answer 21

n! / ((n-k)! k!)

Question 22

permutations in MISSISSIPPI?

Answer 22

11! / 4!4!2!

Question 23

2 strangers get into an empty elevator at the first floor of a building that has 4 floor. Assume that they are equally likely to want to to to floors 2 through 4. Each presses the button for their desired floor. The pressed button or buttons light up. How many light configurations are possible? Are they equally likely?

Answer 23

floor 2, 3,4 <- 9 possibilities
bisa brg” mau ke laintai 2, 3, 4 or mau ke lantai (2,3), (2,4), (3,4)
make the table
2 3 4
2 (2,2) (3,2) (4,2)
3 (2,3) (3,3) (4,3)
4 (2,4) (3,4) (4,4)

Question 24

3 strangers get into an empty elevator at the first floor of a building that has 10 floor. Assume that they are equally likely to want to to to floors 2 through 10. Each presses the button for their desired floor. The pressed button or buttons light up. How many light configurations are possible if consecutive floor?

Answer 24

9 floors, 3 passenger is 9^3 = 727
possibilities: (2,3,4), (3,4,5),(4,5,6),(7,8,9), (8,9,10)
so 7 consecutive possible ways. the order does not matter, so use the formula when other doest not matter with no replacement!