Probability

Question 1

random trial

Answer 1

• process or experiment that has 2+ possible outcomes whose occurrence cannot be predicted with certainty

Question 2

event (of interest)

Answer 2

• any potential subset/options from all the potential outcomes

Question 3

probability

Answer 3

• proportion of times the event would occur if we repeated a random trial over and over again under the same conditions, the true relative frequency
• ranges from 0 - 1

Question 4

proportion

Answer 4

• fraction of individuals having a particular attribute

- (number with attribute)/n

Question 5

mutually exclusive

Answer 5

• 2 events are mutually exclusive if they cannot both be true
• P[A and B] = 0

Question 6

probability distribution (2)

Answer 6

• describes the true relative frequency of all possible values of a random frequency
• list of the probabilities of all mutually exclusive outcomes of a random trial

Question 7

the addition principle

Answer 7

• it two events A and B are mutually exclusive then : P[A OR B] = Pr[A] + Pr[B]

Question 8

what is the probability of an event not occurring?

Answer 8

• Pr[not A] = 1 - Pr[A]

Question 9

general addition rule

Answer 9

• Pr[A or B] = Pr[A] + Pr[B] - Pr[A and B]

Question 10

independence

Answer 10

• two events are independent if the occurrence of one gives no info about whether the second will occur

Question 11

multiplication rule

Answer 11

• if two events A and B are independent, then: Pr[A AND B] = Pr[A] x Pr[B]

Question 12

when probability statements use “OR”

Answer 12

• involves addition: Pr[A or B] = Pr[A] + Pr[B], of the 2 events are mutually exclusive

Question 13

when probability statements use “AND”

Answer 13

• involves multiplication: Pr[A and B] = Pr[A] x Pr[B] when A and B are independent

Question 14

what is the general formulae for “at least one” out of n independent trials

Answer 14

Pr[at least one A] = 1 - (1 - Pr[A])^n

Question 15

dependent events

Answer 15

• probability of one event depends on the outcome of another event

Question 16

conditional probability

Answer 16

• probability of event occurring given that a condition is met
• Pr[X|Y] = probability of X “given” Y

Question 17

general multiplication rule

Answer 17

Pr[A AND B] = Pr[A] * Pr[B|A]

Question 18

law of total probability

Answer 18

the probability of an event, A, is:

Pr[A] = All values of Pr[B] * Pr[A|B]

where B represents all possible mutually exclusive values of the conditions