Presentation on theme: "Beginning Probability"— Presentation transcript:
1Beginning Probability Sample spaceEventDisjoint or Mutually ExclusiveComplement of an EventIndependent EventsBinomial ProbabilityEmpirical vs Theoretical Probability
2Sample Space The set of all possible outcomes! Answer question 1On your paper, list all the events possible for tossing 2 dice.
3An EventAny one or combinations of possible outcomes – a subset of the sample space.
4Answer question 2 Answer question 3 List possibilities, then narrow down to sample space based on restrictions of the question.Answer question 3
5What you want divided by the total. Probability !What you want divided by the total.
6An impossible event An certain event Roll a 7 on one dieP(E) = 0An certain eventFlip a head or tailP(E) = 1
7What is the probability of event F, “rolling a sum of five” on a toss of two dice? Answer question 4
8What is the sample space? (think of the F.C.P. – ways to count) 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
9Disjoint or Mutually Exclusive Events from the same sample space that have no outcomes in commonRolling doubles or a sum of 7
10Disjoint or Mutually Exclusive If events A and B are mutually exclusive, then P(A or B) = P(A) + P(B).Notice the key work “or”Rolling doubles or a sum of 7Answer question 6
11Packy randomly chooses a digit between 0 and 9 (inclusive) 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) =Answer question 7
12If A is an event, then the probability that A does not occur is 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).
13Complement of an EventIf A is an event, then the probability that A does not occur isP(AC) = 1 – P(A).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 An(S) =Answer question 8
14Answer question 9 Answer question 10 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 9Answer question 10
15Getting an A in stats and an A in english Can you think of any more? 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 twiceRoll 2 dice or 1 dice twiceGetting an A in stats and an A in englishCan you think of any more?
16Independent Events or means + and means x If A and B are independent events, thenP(A and B) = P(A) * P(B)Notice the key word “and”You 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?n(S) =Answer question 11Answer question 12Answer question 13
17n(S) = H, T Answer question 14 What is the probability of the outcome HTH when a coin is tossed three times?n(S) = H, TAnswer question 14
18Empirical 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 HeadsVsCalculating P(H) with the formula