Counting Problems

Question 0

Elements of elementary probability theory

Answer 0

Experiment and outcome

Question 1

Denomination

Answer 1

Value of card

Question 2

Sample space

Answer 2

Set of all possible outcomes

Question 3

Sample space symbol

Answer 3

{}

Question 4

Union

Answer 4

Or

Question 5

Disjoint sets

Answer 5

AUB = empty set

Question 6

Mutually exclusive

Answer 6

Events that can’t happen at the same time (disjoint)

Question 7

AU(BNC)=

Answer 7

(AUB)N(AUC)

Question 8

Cardinality

Answer 8

Elements in a set

n(A)

Question 9

Counting multiplication principle

Answer 9

If we have have n independent choices to make, and a different choice in any step results in a different outcome, the number of total outcomes is equal to the product of the number of choices in each step.

Question 10

Permutations

Answer 10

A permutation of n objects is an ordered list of these objects. n!

Question 11

0! =

Answer 11

1

Question 12

nPr

Answer 12

A permutation of n objects taken r at a time

Question 13

nPr =

Answer 13

n!/(n-r)!

Question 14

Distinguishable permutations

Answer 14

Ones we can tell apart

Question 15

Distinguishable presentations formula

Answer 15

n!/(n1!n2!…nk!)

Question 16

Combinations

Answer 16

Select r objects out of a possible n without regard to order.

Question 17

nCr =

Answer 17

nPr/r! (Order irrelevant) = n!/((n-r)!n!) = (n r) = (n n-r)

Question 18

Which choice should we choose first

Answer 18

Choose the choice with a special condition attached to it first

Question 19

What type of sample space do we use in this course?

Answer 19

Finite sample space

Question 20

An experiment can correspond to how many sample spaces?

Answer 20

One or more

Question 21

The more details the more blank the sample space.

Answer 21

Fundamental

Question 22

Event

Answer 22

And event is a subset of sample space S.

Question 23

Simple event

Answer 23

Contains one outcome

Question 24

Compound event

Answer 24

Contains more than one outcome