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:
Beginning Probability Sample space Event Disjoint or Mutually Exclusive Complement of an Event Independent Events Binomial 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 2 Answer question 3
What you want divided by the total.
Roll a 7 on one die Flip a head or tail
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) What events do you want? Answer question 5
Disjoint or Mutually Exclusive Events 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? Whats the sample space? Answer question 7
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).
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).
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 Events Two events are independent events if the occurrence of one has no effect on the probability of the occurrence of the other.
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
What is the probability of the outcome HTH when a coin is tossed three times? Answer question 14
Empirical vs Theoretical Probability The probability you get when you experiment vs the probability the formulas say you get.