Chapter 5

Question 1

Probability

Answer 1

The probability of an event is its true relative frequency. This is the proportion of times the event would occur if we repeated the same process over and over again.

Question 2

Mutually exclusive events

Answer 2

There are no overlap between two event. Two things can’t occur in one event.
PR[A & B] = 0

Question 3

Non-exclusive events

Answer 3

There are some overlaps between two things. Same thing can be achieved by both parties.
Pr[A & B) does not 0

Question 4

Probability distribution

Answer 4

A probability distribution is the true relative frequency of all possible values of a random sample - describes discrete variables

Question 5

Proportion

Answer 5

The proportion is the number of times an event occurs divided by the number of tries.

Question 6

Probability rule #1

Answer 6

General: Pr[A or B] = Pr[A] + Pr[B] - Pr[A and B]
Mutually exclusive: Pr[A or B] = Pr[A} + Pr[B]

Question 7

Probability rule #2

Answer 7

General: Pr[A & B] = Pr[A] x Pr[B|A]. The probability of one event times the probability of the other, conditioned on the first.

Question 8

Independent

Answer 8

Two events are independent if the occurrence of one gives no information about whether the second will occur.
A & B are independent
- if Pr[B|A] = Pr[B]
- if Pr[A & B] = Pr[A] x Pr[B]

Question 9

Dependent

Answer 9

Events are dependent when the probability of one event depends on the outcome of another
Pr[A & B] does not equal Pr[A] x Pr[B]

Question 10

Bayes Theorem

Answer 10

The probability of A given B equals the probability of B given A time the probability of A divided by the probability of B.
The Bases theorem is used to translate between probabilistic statement