Ch 7 Probability

Question 1

Event/Outcome

Answer 1

-A subset of the sample space

bag of 3 different coloured balls
-obtaining a blue ball (event/outcome A)
-obtaining a red ball (event/outcome B)
etc

Question 2

Sample Space

Answer 2

A set of all possible events

Question 3

Probability

Answer 3

is the likelihood of something happening in the future. It is expressed as a number between zero (can never happen) to 1 (will always happen). It can be expressed as a fraction, a decimal, a percent, or as “odds”.

Question 4

Probability Rules

Answer 4

1. 0 greater than or equal to P(A) less then equal to 1

2. P(Sample space) = 1

Question 5

How to avoid slipping (in probability)?

Answer 5

1. always think about discrete probability as a proportion (a set of events and a sample space of possible events)
2. Interleave different kinds of probability exercises into your practice

Question 6

P(A): Marginal probability

Answer 6

the probability of A

Question 7

P(A): Marginal probability

Answer 7

the probability of A

- P(A)= NAi/N
e. g., 6blue balls/20 balls total= 0.30

Question 8

P(A’): A Complement

Answer 8

the probability of not A

- P(A’)= 1-P(A
e. .g, P(blue’) = 1-(P(blue)= 1-0.3= 07)

Question 9

P(AuB): Union

Answer 9

the probability of A or B

Question 10

P(A|B): Conditional Probability

Answer 10

the probability of A given B

Question 11

P(A|B): Conditional Probability

Answer 11

the probability of A given B

- P(AnB)/ P(B)

Question 12

Mutually exclusive events

Answer 12

if the events cannot both be true (occur). A clear example is the set of outcomes of a single coin toss, which can result in either heads or tails, but not both.

Question 13

Independent events

Answer 13

the probability that one event occurs in no way affects the probability of the other event occurring. An example of two independent events is as follows; say you rolled a die and flipped a coin

Question 14

Dependent events

Answer 14

the occurrence of event A tells us something about the occurrence of event B (i.e., it affects its probability of occurring and vice verse)
-(ex, taking a ball out of bag without replacement. Each ball taken out now affects the sample space, thus, affecting probability of other events occurring)

Question 15

Additive rules of probability

Answer 15

• If 2 discrete events, A & B are mutually exclusive, P(AuB)= P(A) + P(B)
• If independent or dependent: P(AuB) = P(A) + P(B)-P(AnB)

Question 16

Multiplicative rule of probability

Answer 16

-If 2 discrete events, A & B, are independent, P (AnB)= P(A) x P(B)