Beginning Probability Sample space Event Disjoint or Mutually Exclusive Complement of an Event...
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Transcript of Beginning Probability Sample space Event Disjoint or Mutually Exclusive Complement of an Event...
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