Probability The likelihood that an event will occur

Probability • The likelihood that an event will occur. • A number from 0 to 1 • As a percent from 0% to 100%

Theoretical Probability: The number of ways that an event can occur, divided by the total number of outcomes in the sample space. Example: Find the probability of flipping a heads on a coin. Example: Find the probability of getting an even number when you roll a die.

Compound Probability A compound event combines two or more events, using the word and or the word or.

AND: A nd Then M ultiply Means you MULTIPLY

OR: OR Means you ADD OAR D D

Mutually Exclusive vs. Overlapping If two or more events cannot occur at the same time they are termed mutually exclusive. They have no common outcomes. Overlapping events have at least one common outcome.

Mutually Exclusive Events For mutually exclusive events, the probability that one or the other of several events will occur is found by summing the individual probabilities of the events: P(A or B) = P(A) + P(B) A Venn diagram is used to show mutually exclusive events.

Mutually Exclusive Events 1) Find the probability that a girl’s favorite department 0. 45 store is Macy’s or Nordstrom. 2) Find the probability that a girl’s favorite store is not JC Penny’s. 0. 90 Macy’s Saks Nordstrom JC Pennys Bloomingdale’s 0. 25 0. 20 0. 10 0. 25

1 1 2 3 4 5 6

1 2 3 4 5 6 7 8 9 4 5 6 7 8 9 10 11 12

Mutually Exclusive Events 3) When rolling two dice, what is probability that your sum will be 4 or 5? 1 2 3 4 5 6 4 5 6 7 8 9 10 5 6 7 8 9 10 11 12 1 2 3 7/36

Mutually Exclusive Events 4) When rolling two dice, what is the probability that your sum will be an even number or a five? 1 2 3 4 5 6 4 5 6 7 8 9 10 5 6 7 8 9 10 11 12 1 2 3 11/18

Mutually Exclusive Events 5) When rolling two dice, what is the probability that your sum will be a number less than 4 or greater than 10? 1 2 3 4 5 6 4 5 6 7 8 9 10 5 6 7 8 9 10 11 12 1 2 3 1/6

Mutually Exclusive Events 6) What is the probability of picking a queen or an ace from a deck of cards 2/13

Mutually Exclusive Events 7) What is the probability of picking a face card or an ace from a deck of cards? 4/13

Mutually Exclusive Events 8) What is the probability of picking a red or a black card from a deck of cards? 1

Mutually Exclusive Events 9) What is the probability of picking an even card or a face card from a deck of cards? 8/9

Intersection of 2 Events Denoted by the symbol: A B Is the event containing all elements that are COMMON to both A and B

Overlapping events have at least one common outcome. You will have to SUBTRACT out the overlapping amount

Overlapping Events Probability that non-mutually exclusive events A and B or both will occur expressed as: P(A or B) = P(A) + P(B) – P(A B)

Overlapping Events 10) Find the P(A B) 29/48

Example 11) Find the P(female or FL) out of the committee members listed in the table. Fem Male FL 8 4 AL 6 3 GA 7 3

Example 12) Find the P(King Clubs)?

13) When rolling 2 dice, what is the probability of getting an even sum or a sum greater than 10? 1 2 3 4 5 6 4 5 6 7 8 9 10 5 6 7 8 9 10 11 12 1 2 3

Complementary Events The complement of an event is the set of outcomes in the sample space that are NOT included in the outcomes of the event. The complement is denoted with the word “not, ” or with the ' or symbol.

Complementary Events 14) What is the probability not being in the band or a club? 1 - 29/48 =19/48

Complementary Events 15) What is the probability that a female does not play volleyball? 1 - 26/454 = 214/227

Class Example A = people in a Science Class B = people in an English Class A B

Homework!