Discrete Random Variables M2A:1

Question 1

The chance that something will happen is expressed in fractions, decimals, or percents

Answer 1

Probability

Question 2

A set of possible outcomes from an experiment

Answer 2

Sample space

Question 3

One or more of the possible outcomes of doing something

Answer 3

Event

Question 4

What is mutual exclusivity?

Answer 4

Events that can only take place one at a given time. (Heads or tails)

Question 5

If A and B have no sample space outcomes in common they are said to be what?

What is the equation?

Answer 5

Mutually exclusive

P(A (upside down U) B)=0

Question 6

What are the 3 types of probability

Answer 6

1. Classical
2. Relative frequency occurance
3. Subjective

Question 7

Statements of probability based on reasoning before any experiment takes place is called ?

Answer 7

P(A)= # of occurrences of A
————————————
Total # of possible outcomes

Classical reasoning (probability)

Question 8

Proportion of times that an event occurs in the long run when conditions are stable—observed relative frequency of an event in a very large number of trials (Historical)

Example

Answer 8

Relative frequency of occurrence probability

Amount of As historically in a class to determine the likelihood of As in the past

Question 9

The probability assigned to an event in the basis of whatever evidence is available- the decision maker can assign biases to manipulate evidence

Answer 9

Subjective probability

Weather man says it will rain

Question 10

Classical probability is also known as this

It must have a total of what?

Answer 10

Also known as a Priori probability and objective probability

Must equal to 1.00 because all outcomes are known.

Question 11

Types of classical probability are what?

Answer 11

1. Marginal probability- the probability of a single event- P(A)
2. Joint probability- the probability of two or more events occurring simultaneously or in sequence- P(AB)
3. Conditional probability- the probability of an event A occurring, given that B has already occurred P(A|B)

Question 12

What is a complement or Ā?

Answer 12

Ā of an event is the set of all sample space outcomes not in A

P(Ā)= 1-P(A)

Question 13

When are things statistically independent?

Answer 13

One event has no effect on probability on another event occurring

Question 14

What is conditional probability?

P(A|B)

Answer 14

The probability of an event A, given that the event B has occurred, is called the conditional probability

Question 15

Drawing a red marble from a bag that contains 50% red marbles and 50% white marbles.

What is the probability?

What type of probability?

Answer 15

Marginal probability because it is the probability of a single event

Answer P(R)= 50%

Question 16

Drawing a red marble 7 times in succession with replacement from the bag containing 90% red marbles and 10% white marbles.

What is the probability?

What type of probability?

Answer 16

Joint probability

P(RRRRRRR) = (0.9)^7 = 0.48

Question 17

Drawing a red marble from a bag containing 50% red marbles and 50% white marbles given last drawing you selected a red marble with replacement

What is the probability

What type of probability

Answer 17

Conditional probability under statistically independent conditions

50%

P(R|R) = P(R) = 50%

Question 18

Two events are said to be what if and only if:

P(A|B)=P(A)

This is equivalent to

P(B|A) = P(B)

And assumes P(A) and P(B) greater than zero

Answer 18

Independent

Question 19

The joint probability of A and B (the intersection of A and B) will occur is:

P(A Û B) = P(A) x P(B|A) = P(B) x P(A|B)

If A and B are independent then the probability that both A and B will occur is

P(AûB)= P(A) x P(B|A) = P(B) z P(A)

What is this ?

Answer 19

The multiplication rule