7.1 An intro to Discrete Probability

Question 1

Probability vocab:

Answer 1

1. Experiment
2. Sample Space.
3. event

Question 2

experiment:

Answer 2

A procedure that yields one of the given set of possible outcomes.

Question 3

Sample space and event:

Answer 3

Sample space: set of possible outcomes.

Event: subset of Sample space.

Question 4

Laplace’s definition of the probability of an event with finitely many possible outcomes:

Answer 4

If S is a finite nonempty sample space of equally likely outcomes, and E is an event, that
is, a subset of S, then the probability of E is
p(E) = |E|/|S|

Question 5

THM:

probability of complement

proof too

Answer 5

Let E be an event in a sample space S. The probability of the event E = S − E, the complementary event of E, is given by
p(E) = 1 − p(E).

Question 6

Probability of Union:

proof too

Answer 6

Let E1 and E2 be events in the sample space S. Then

p(E1 ∪ E2) = p(E1) + p(E2) − p(E1 ∩ E2).

Question 7

Probabilistic reasoning

Answer 7

A common problem is determining which of two events is more likely.

Think of the monty hall 3 door puzzle.