Chapter 3 Probability

Question 1

Probability

Answer 1

Probability- is the measure of the likeliness that an event will occur.

Question 2

Event

Answer 2

Event – A subset in the set of all outcomes of an experiment. In other words, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned.

Ex. Getting a Tail when tossing a coin; Rolling a “7” with two dice

Question 3

Sample space

Answer 3

Sample space – The set of all outcomes of an experiment is called a sample space and denoted usually by S. In other words, All the possible outcomes of an experiment.

Ex. choosing a card from a deck There are 52 cards in a deck (not including Jokers)

So the Sample Space is all 52 possible cards: {Ace of Hearts, 2 of Hearts, etc… }

Question 4

Probability OR

Answer 4

Question 5

Probability AND

Answer 5

A = {1,2,3,4,5}

B = {4,5,6,7,8}

Question 6

Probability COMPLETMENT

Answer 6

Question 7

Notation for Probabilities

Answer 7

Question 8

Probability (formal def)

Answer 8

Question 9

Mutually Exclusive Events

Answer 9

Mutually exclusive events - can’t happen at the same time.

”"”P(A ∩ B) = 0 means event A & B are mutually Exclusive”!!!”“

Ex. Cards: Kings and Aces Are Mutually Exclusive.

Kings and Hearts are not, because we can have a King of Hearts!

Question 10

Some Rules of Probability

The special addition rule:

Answer 10

Question 11

Some Rules of Probability

The Complementation Rule:

Answer 11

Question 12

Some Rules of Probability

The General Addition Rule:

Answer 12

Question 13

Conditional Probability

Answer 13

Conditional Probability:The likelihood that an event will occurgiven that another event has already occurred. The conditional probability of A Given B is written P(A|B) In other words, Events can be “Independent”, meaning each event is not affected by any other events.

Note: in words P(A|B) means the probability of event A, given that event B has already occurred.

Question 14

Independent Events

Answer 14

Independent Events - Two events are independent if the following are true

1.) P(A | B) = P(A ∩ B) / P(B)

2.) P(B | A) = P(A ∩ B) / P(A)

3.) P(A ∩ B) = P(A) * P(B)

Question 15

Equally Likely

Answer 15

Equally Likely: Each outcome of an experiment has the same probability.

Question 16

Outcome (observation)

Answer 16

Outcome (observation): A particular result of an experiment.

Question 17

Venn Diagram

Answer 17

Venn Diagram - A Venn diagram is a picture that represents the outcomes of an experiment. It generally consists of a box that represents the sample space S together with circles or ovals. The circles or ovals represent events.

Question 18

Intersection(Venn Diagram)

Answer 18

Intersection: Members of both set A and set B

Question 19

Union(Venn Diagram)

Answer 19

Union: Members of set A or set B or both

Question 20

Complementary(Venn Diagram)

Answer 20

Complementary: Members not in the set

Question 21

Universal Set(Venn Diagram)

Answer 21

Universal Set: All members

Question 22

Subset(Venn Diagram)

Answer 22

Subset: All members of set A are in set B

Question 23

Fundamental Counting Principle

Answer 23

Fundamental Counting Principle – using multipltion to quickly count the of ways certain things can happen if M can occur in m ways and is followed by N that can occur in n ways, than M followed by N can occur in m * n ways.

is a way to figure out the number of outcomes in a probability problem. Basically, you multiply the events together to get the total number of outcomes. The formula is:

If you have an event “a” and another event “b” then all the different outcomes for the events is a * b.

Question 24

Permutations

Answer 24

Permutations – Any of the ways we can arrange things, where the order is important.. Placement and Position matter.(counting different ways to arrange things in order.)

Question 25

Permutation with repetition (with replacement)

formula

Answer 25

Permutation with repetition (with replacement)

Question 26

Permutations without repetition (without replacement)

formula(always use)

Answer 26

Permutations without repetition (without replacement)

Question 27

Factorial

Answer 27

Factorial – multiply a series of descending natural numbers

Question 28

Combinations

Answer 28

Combinations –Any of the ways we can combine things, when the order does not matter. Couldn’t care less (counting groups)

Question 29

Combination without repetition

formula

Answer 29

Combination without repetition

Question 30

There are 20 balls, 14 blue and 6 green. Find the probability that of the following without replacement:

1. P(blue 1^st , blue 2^nd ) =
2. P(blue 1^st , green 2^nd ) =
3. P(green 1^st , green 2^nd ) =
4. P(green 1^st , blue 2^nd ) =
5. P( getting a blue on the 2^nd) =

Answer 30

There are 20 balls, 14 blue and 6 green. Find the probability that of the following without replacement:

1. P(blue 1^st , blue 2^nd ) =
2. P(blue 1^st , green 2^nd ) =
3. P(green 1^st , green 2^nd ) =
4. P(green 1^st , blue 2^nd ) =
5. P( getting a blue on the 2^nd) = .70

Question 31

Question on Combination & Premutation

Answer 31

Answer Key