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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
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