Simple Probability Things to know and do: Probabilities may be interpreted as expected (Theoretical) or empirical (Experimental) percentages. Be able to list the sample space of a simple experiment. Be able to find probabilities given a defined success and a sample space. Find theoretical probabilities given a description of ratios in the sample space. Know how to compute odds Be able to find probabilities, including conditional probabilities from a contingency table Be able to apply the multiplication rule and the addition rule. A die has six sides. A deck of cards has 52 cards, 13 cards of each suite, four cards of each rank. There are 12 face cards in a deck of cards, four each of jack, queen and king. In the game rock, paper, scissors, each player chooses to be a rock, paper or scissors. Winners are determined by: Rock crushes scissors, paper covers rock and scissors cut paper.

The grades of students in Mr. Gillam’s class break down as follows: Simple Probability Examples: The grades of students in Mr. Gillam’s class break down as follows: A: 10%, B: 20%, C:30%, D:30%, F:10% If Mr. Gillam teaches 1000 students, how many A’s would you expect? How many passing grades? What are the odds against failing?

The grades of students in Mr. Gillam’s class break down as follows: Simple Probability Examples: The grades of students in Mr. Gillam’s class break down as follows: A: 10%, B: 20%, C:30%, D:30%, F:10% If Mr. Gillam teaches 1000 students, how many A’s would you expect? 1000*.1 = 100 How many passing grades? 1000 - #F = 900 What are the odds against failing? 9:1 against

List the sample space for flipping a coin twice: Simple Probability Example: List the sample space for flipping a coin twice: Complete this chart: #heads F P(x) 1 2 TOTAL 4

List the sample space for flipping a coin twice: Simple Probability Example: List the sample space for flipping a coin twice: HH, HT, TH, TT Complete this chart: #heads F P(x) 1 ¼ 2 ½ TOTAL 4

Simple Probability Example: There are twice as many C’s as A’s, there are the same number of B’s as A’s. There are half as many D’s as B’s. There are no F’s What is P(C )? Let x be the number of A’s: F P(x) A X 1/(4.5)=.22 B 1/(4.5) =.22 C 2x 2/(4.5)=.44 D .5x .5/(4.5)=.22 t 4.5x

Simple Probability Example: Rolls in mud Does not roll in mud Pig 50 10 Not pig 20 70 What is the probability that an animal is a pig? What is the probability that an animal is a pig and rolls in mud? What is the probability that an animal is a pig, given it rolls in mud?

Simple Probability Example: Rolls in mud Does not roll in mud Pig 50 10 60 Not pig 20 70 90 80 150 What is the probability that an animal is a pig? 60/150 = 2/5 What is the probability that an animal is a pig and rolls in mud? 50/150=1/3 What is the probability that an animal is a pig, given it rolls in mud? 50/70=5/7

Simple Probability Example: What is the probability of drawing a face card from a regular deck of cards in a single draw? What is the probability of drawing a face card or a seven from a deck of cards in one draw? What is the probability of drawing a face card or a diamond from a deck of regular cards? What is the probability of drawing a face card and a seven in two draws without replacement?

Simple Probability Example: What is the probability of drawing a face card from a regular deck of cards in a single draw? 12/52 What is the probability of drawing a face card or a seven from a deck of cards in one draw? 12/52 + 4/52 – 0 = 16/52 What is the probability of drawing a face card or a diamond from a deck of regular cards? 12/52 + 13/52 – 3/52 = 22/52 What is the probability of drawing a face card and a seven in two draws without replacement? 12/52*4/51