Probability

Question 1

What are the two fundamental ways we can determine probability?

Answer 1

1. theoretical (aka classical)

2. emperical (aka observational)

Question 2

When are classical methods of probability used?

Answer 2

games of chance

Question 3

Why is theoretical method also called classical

Answer 3

because their values are determined by the game itself (the nature of the situation… 6 sided dice)

Question 4

What is probability?

Answer 4

a way of quantifying uncertainty

Question 5

What do empirical methods use to determine probability?

Answer 5

series of random experiments/trials to produce outcomes that cannot b predicted in advance

Question 6

When a simulation is run or a random sample is used and the results recorded, is theoritical or empirical probability in play?

Answer 6

empirical

Question 7

What is the relative frequency of probability

Answer 7

using empiracal probability (simulations, etc) to prove the theoretical probability

Question 8

what is the formula for relative frequency?

Answer 8

number of times A occurred / total number of repetitions

Question 9

What is the Law of Large Numbers?

Answer 9

the relative frequency of an event does approach the theoretical probability of that event as the number of repetitions increases

Question 10

What is a sample space?

Answer 10

A list of all possible outcomes the random experiment can produce

Question 11

What are the 11 basic probability rules?

Answer 11

1. For any event A, 0 ≤ P(A) ≤ 1
2. P(S) = 1
3. Compliment rule: P(not A) = 1 - P(A)
   or
   P(A) = a - P(not A)
4. If A and B are disjoint events, then P(A or B) = P(A) + P(B)
5. If A and B are independent, then P(A and B) = P(A) * P(B)
6. General Addition Rule: For any 2 events A and B, P(A or B) = (PA) + P(B) - P(A and B)
   or if disjoint:
   P(A or B) = P(A) + P(B)
7. Multiplication Rule for Independent Events: P(A and B) = P(A) * P(B)

Question 12

What does Probability rules 1: 1. For any event A, 0 ≤ P(A) ≤ 1 mean?

Answer 12

that the probability of any event can range between 0 and 1

Question 13

What does Rule 2: P(S) = 1 mean?

Answer 13

the sum of all the probabilities of all possible outcomes is 1

Question 14

What does Rule 3: P(not A) = 1 - P(A) mean?

Answer 14

probability that an event does not occur is 1 minus the probability that it does occur

Question 15

What is disjoint or mutually exclusive?

Answer 15

when two events cannot occur at the same time

Question 16

What does Rule 4: If A and B are disjoint events, then P(A or B) = P(A) + P(B) mean?

Answer 16

If the two events are disjoint, and you are looking for the probability of A or B occurring, then P(A) and P(B)

Question 17

In probability, does “or” mean multiplication, division or addition?

Answer 17

addition

Question 18

What does rule 5: P(A and B) = P(event A occurs and event B occurs) mean

Answer 18

means you find the the overlap of these two probabilities occurring at the same time

Question 19

in probability, does “and” mean division, multiplication or addition?

Answer 19

multiplication

Question 20

If two events are disjoint, what would be P(A and B)

Answer 20

0, because they cannot occur at the same time

Question 21

Define independent events

Answer 21

if the fact that one event occurs and it does not affect the probability that the other event will occur

Question 22

If two events are not disjoint, but are independent, will P(A and B) be greater than 0

Answer 22

yes, because they can still occur at the same time, they just have no affect on each other.

Question 23

If two events are disjoint, can they be independent?

Answer 23

if two items cannot occur at the same time, then they can’t have a direct affect on each other.

Question 24

What rule(s) can be used when finding “at least one of”

Answer 24

1. compliment rule:

P(at least one of several events occur) = 1-P(none of the events occur)

Question 25

How is conditional probability notated:

Answer 25

(A | B)
A = the probability we seek
B = the given

Question 26

What is the formula for conditional probability?

Answer 26

P(B|A) = (A and B) / P(A)

always divide by the given event

Question 27

How can you determine if two events are dependent on each other (4)

Answer 27

Compare:
1. P(A | B) and P(A)

2. P(A | B) and P(A | not B)
3. P(B | A) and
   P(B | not A)
4. P(A and B) = P(A) * P(B)

Question 28

What is the general multiplication rule for dependent events?

Answer 28

P(A and B) = P(A) * P(B|A)