01 Probability

Question 1

You __(v.)__ a coin (2 answers)

Answer 1

Toss; flip

Question 2

♡♧♢♤ are the four __(n.)__ in a pack of __(n.)__

Answer 2

Suits in a pack of playing cards

Question 3

The King, Queen, and Jack in a pack of cards are called the __(n.)__ cards

Answer 3

Face cards

Question 4

⚂ is a __(n.)__

Answer 4

a die

Question 5

⚂⚄ are __(n., pl.)__

Answer 5

dice (not dies)

Question 6

You __(v.)__ a die

Answer 6

roll or throw

Question 7

Random means…

Answer 7

• each individual outcome is unpredictable or uncertain
• there is a pattern over many repetitions

Question 8

What is an experiment?

Answer 8

Any phenomenon with random results

Question 9

What is the sample space, S, of an experiment?

Answer 9

The set of all possible outcomes

Question 10

What is an event?

Answer 10

A subset of the sample space; a set of one or more possible outcomes

Question 11

If A is an event, what is P(A)?

Answer 11

The probability of the event A occurring

Question 12

What is the definition of the probability of an outcome?

Answer 12

The long-term relative frequency of the outcome; the proportion of times the outcome would occur in a long series of repetitions

Question 13

What is the definition of experimental probability?

Answer 13

P(A) = the number of times the desired outcome occurs / the total number of trials

Question 14

What is a trial?

Answer 14

A repetition of a phenomenon with random results.

For example, each roll of a die is a trial

Question 15

What is a distribution?

Answer 15

The pattern of frequencies of the different possible outcomes to a random phenomenon

Question 16

What is theoretical probability?

Answer 16

If there are k individual outcomes to an event, and each is equally likely, then the theoretical probability of each outcome is 1/k.

Question 17

What is a fair/unbiased coin/die?

Answer 17

One in which each possible outcome is equally likely

Question 18

A probability model consists of two parts; what are they?

Answer 18

• A sample space, S
• a means of assigning probabilities to events

Question 19

What are the four suits in a pack of playing cards called?

Answer 19

• ♡ Hearts
• ♧ Clubs
• ♢ Diamonds
• ♤ Spades

Question 20

What does it mean if events or trials are independent?

Answer 20

The outcome of one event or trial does not affect the outcome of any other event or trial.

Question 21

What does it mean to say that two events are mutually exclusive or disjoint?

Answer 21

They cannot occur together;

eg “passing the exam” and “failing the exam” are disjoint events - it is not possible to both pass and fail the exam.

Question 22

What does {A∪B} mean?

Answer 22

“A union B” is the set of all outcomes which are in either A or B (or both).

Question 23

What does {A∩B} mean?

Answer 23

“A intersect B” is the set of all outcomes that are both A and B.

Question 24

If A and B are mutually exclusive or disjoint, then we can say something about either {A∪B} or {A∩B}; what?

Answer 24

{A∩B} = ∅, or A intersect B is empty.

Question 25

What is the General Addition Rule for P(A or B)?

Answer 25

P(A or B) = P(A∪B) = P(A) + P(B) - P(A∩B)

Question 26

What is the multiplication rule for P(A or B) and when is it valid?

Answer 26

P(A or B) = P(A∩B) = P(A)⋅P(B),

if A and B are independent events.

Question 27

What is conditional probability?

Answer 27

The situation where the probability of a second event is dependent on the outcome of a first event.

For example, the probability of the event “snow falls on a day” depends on the outcome of the event “the day is in winter.”

Question 28

Conditional probability is defined as P(B|A) =…?

Answer 28

The probability of B given A,
P(B|A) = P(A∩B)/P(A).

Question 29

If A and B are independent events, what can we say about them?

Answer 29

P(B|A) = P(B); the conditional probability of B given A is the same as the probability of B
also
P(A∩B) = P(A)⋅P(B)

Question 30

How many different groups of size r can you make from n objects? (the order of the objects is not important)

Answer 30

• “n choose r” = _nC_r = n! / r!(n-r)!
• each of these groups is called a combination

Question 31

How many different groups of size r can you make from n objects if the order of the objects is important?

Answer 31

• _nP_r = n! / (n-r)!
• each of these groups is called a permutation

Question 32

What tool can you use to help you calculate probabilities in a complex situation?

Answer 32

A tree diagram

Question 33

What is Benford’s law?

Answer 33

The distribution of the first digits of numbers in accounting records - the 9 possible first digits do not have equal probability of occurring; 1 is the most common first digit, then 2, then 3…

Question 34

What are the 5 key facts to remember about probability?

Answer 34

• P(A) = number of desired outcomes / total number of trials
• independent events are events whose outcomes do not affect each other
• mutually exclusive events are events which cannot occur together
• P(A or B) = P(A) + P(B) - P(A and B)
• if A and B are independent, P(A and B) = P(A)⋅P(B)