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.

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

What you want divided by the total. Probability ! What you want divided by the total.

An impossible event An certain event Roll a 7 on one die P(E) = 0 An certain event Flip a head or tail 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 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

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 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 7 Answer question 6

Packy 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) = 0 1 2 3 4 5 6 7 8 9 Answer question 7

If A is an event, then the probability that A does not occur is Complement of an Event The 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 is P(AC) = 1 – P(A).

Complement of an Event If A is an event, then the probability that A does not occur is P(AC) = 1 – P(A). A = a digit that is greater than 6 or is a multiple of 6 then P(Ac) = Look at all the events that aren’t part of A n(S) = 0 1 2 3 4 5 6 7 8 9 Answer question 8

Answer 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 9 Answer question 10

Getting an A in stats and an A in english Can you think of any more? Independent Events Two 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 Events or means + and means x 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? n(S) = 0 1 2 3 4 5 6 7 8 9 Answer question 11 Answer question 12 Answer question 13

n(S) = H, T Answer question 14 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 Heads Vs Calculating P(H) with the formula