Beginning Probability

Sample spaceEvent

Disjoint or Mutually ExclusiveComplement of an Event

Independent EventsBinomial Probability

Empirical vs Theoretical Probability

Sample Space• The set of all possible outcomes!– Answer question 1

• On your paper, list all the events possible for tossing 2 dice.

An Event• Any one or combinations of possible outcomes

– a subset of the sample space.

List possibilities, then narrow down to sample space based on restrictions of the question.

Answer question 2Answer question 3

PROBABILITY !What you want divided by the total.

)(

)()(

Sn

EnEP

An impossible event

An certain event

Roll a 7 on one die

Flip a head or tail

P(E) = 0

P(E) = 1

What is the probability of event F, “rolling a sum of five” on a toss of two dice?

Answer question 4

What is the probability that a five-digit telephone number chosen at random has no repeated digits?

What is the sample space? (think of the F.C.P. – ways to count)

n(S) = _ _ _ _ _ = What events do you want?

n(E) = _ _ _ _ _ =Answer question 5

Disjoint or Mutually ExclusiveEvents from the same sample space that have no outcomes in common

Rolling doubles or a sum of 7

Disjoint or Mutually Exclusive

Rolling doubles or a sum of 7

Answer question 6

If events A and B are mutually exclusive, then P(A or B) = P(A) + P(B).Notice the key work “or”

Packy randomly chooses a digit between 0 and 9 (inclusive). What is the probability that Packy will choose a digit that is greater than

6 or is a multiple of 6? What’s the sample space?

n(S) = 0 1 2 3 4 5 6 7 8 9Answer question 7

Complement of an EventThe complement of the event A, denoted Ac, is the set of all

outcomes in the sample space that are not in event A.

If A is an event, then the probability that A does not occur isP(AC) = 1 – P(A).

Complement of an Event

A = a digit that is greater than 6 or is a multiple of 6then P(Ac) =

Look at all the events that aren’t part of A

Answer question 8n(S) = 0 1 2 3 4 5 6 7 8 9

If A is an event, then the probability that A does not occur isP(AC) = 1 – P(A).

In the game of contract bridge, each player is dealt a 13-card hand from a standard deck of 52 cards. What is the probability that a bridge hand has at least 1 heart?

Answer question 9

Answer question 10

Independent EventsTwo events are independent events if the occurrence of one has no effect on the probability of the occurrence of

the other.

Flip a coin twice

Roll 2 dice or 1 dice twice

Getting an A in stats and an A in english

Can you think of any more?

Independent EventsIf A and B are independent events, then

P(A and B) = P(A) * P(B)Notice the key word “and”

or means +

and means xYou develop a program to generate random digits. What is

the probability that the first digit generated is even and the second is a multiple of 3?

Are the two events independent?

Answer question 11n(S) = 0 1 2 3 4 5 6 7 8 9

Answer question 12Answer question 13

What is the probability of the outcome HTH when a coin is tossed three times?

n(S) = H, T

Answer question 14

Empirical vs Theoretical Probability

The probability you get when you experiment vs the probability the

formulas say you get.

Tossing a coin 20 times to see % of HeadsVs

Calculating P(H) with the formula