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Beginning Probability Sample space Event Disjoint or Mutually Exclusive Complement of an Event Independent Events Binomial Probability Empirical vs Theoretical.

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Presentation on theme: "Beginning Probability Sample space Event Disjoint or Mutually Exclusive Complement of an Event Independent Events Binomial Probability Empirical vs Theoretical."— Presentation transcript:

1 Beginning Probability Sample space Event Disjoint or Mutually Exclusive Complement of an Event Independent Events Binomial Probability Empirical vs Theoretical Probability

2 Sample Space The set of all possible outcomes! – Answer question 1 On your paper, list all the events possible for tossing 2 dice.

3 An Event Any one or combinations of possible outcomes – a subset of the sample space.

4 List possibilities, then narrow down to sample space based on restrictions of the question. Answer question 2 Answer question 3

5 What you want divided by the total.

6 Roll a 7 on one die Flip a head or tail

7 What is the probability of event F, rolling a sum of five on a toss of two dice? Answer question 4

8 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) What events do you want? Answer question 5

9 Disjoint or Mutually Exclusive Events from the same sample space that have no outcomes in common Rolling doubles or a sum of 7

10 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

11 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? Whats the sample space? Answer question 7

12 Complement of an Event The complement of the event A, denoted A c, 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 is P(A C ) = 1 – P(A).

13 Complement of an Event A = a digit that is greater than 6 or is a multiple of 6 then P(A c ) = Look at all the events that arent part of A Answer question 8 A does not occur If A is an event, then the probability that A does not occur is P(A C ) = 1 – P(A).

14 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

15 Independent Events Two events are independent events if the occurrence of one has no effect on the probability of the occurrence of the other.

16 Independent Events If A and B are independent events, then P(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? Answer question 11 Answer question 12 Answer question 13

17 What is the probability of the outcome HTH when a coin is tossed three times? Answer question 14

18 Empirical vs Theoretical Probability The probability you get when you experiment vs the probability the formulas say you get.


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