Understanding Chance

Question 1

The probability of something:

Answer 1

P(Event) = 1 − P(Complement event)

Question 2

Conditional probability

Answer 2

the chance that a certain event (1) occurs, given another event (2) has occurred.
* P(Event 1|Event 2)

Question 3

Multiplication Rule

Answer 3

The probability that two events occur is the chance of the 1st event multiplied by the chance of the 2nd event, given the 1st has occurred.
* P(Event1 and Event2) = P(Event1) × P(Event2 | Event1)

Question 4

Addition Rule

Answer 4

The probability at least one of two events occurs is the chance of the 1st event plus the chance of the 2nd event minus the probability that both events occur.
* P(Event1 or Event2) = P(Event1) + P(Event2) − P(Event1 and Event2)

Question 5

Mutually exclusive

Answer 5

Two events are mutually exclusive when the occurrence of one event prevents the occurence of the other.

Question 6

Independence

Answer 6

Two events are independent if the chance of the 1st given the 2nd is the same as the 1st, i.e.
* P(Event 1 | Event 2) = P(Event 1)

Question 7

Prosecutor’s fallacy

Answer 7

it is assumed that the probability of a random match is equal to the probability that the defendant is innocent.
* P(A⼁B) = P(B⼁A)

Question 8

Drawing randomly with replacement ensures…

Answer 8

independence

Question 9

Drawing randomly without replacement implies…

Answer 9

dependence

Question 10

Probability of paths can be added because…

Answer 10

events are mutually exclusive (if you throw (1,5) you can’t have thrown (2,4) at the same time)

Question 11

sample()

Answer 11

draws random samples from a collection of objects that you tell R
sample( # we want: # of possible, size = # , replace = T)

Question 12

replicate

Answer 12

replicate( how many times, function() )

Question 13

function()

Answer 13

list of commands that you use to define a particular function