3 Types of Probabilities

3 Types of Probabilities 1. Classical Probability Uses sample spaces to determine the numerical probability that an event will occur n(E) n(S) P(E) =

3 Types of Probabilities 2. Empirical Probability Relies on actual experience to determine the likelihood of outcomes _f_ n P(E) =

3 Types of Probabilities Classical Probability & Empirical Probability Difference between Classical Probability & Empirical Probability Classical probability assumes that certain outcomes are equally likely

3 Types of Probabilities 3. Subjective Probability Probability based on an educated guess or estimate I think…

What is the Complement of an Event E? (Review) What is the Complement of an Event E? Set of outcomes in the sample space that are not included in the outcomes of event E Symbol- E’ (Also can be seen as E) _

Complement of an Event E (Review) Complement of an Event E Rolling a die Let E = even # P (E) 1 2 3 4 6 5 P (E’)

What is Mutually Exclusive? (Review) What is Mutually Exclusive? Two events that have no outcomes in common.

are Mutually Exclusive? Which of the following are Mutually Exclusive?

Are the two events mutually exclusive or not? 1. Selecting a skittle from a bag of skittles, P(purple or red) Ask yourself: Can a skittle be both purple and red at the same time? NO! P( or ) = ? Mutually Exclusive

Are the two events mutually exclusive or not? 2. Looking at jeeps, P(4WD or big tires) Jeeps with big tires Jeeps that are 4WD

Yeah! NOT Mutually Exclusive 2. Looking at jeeps, P(4WD or big tires) Are the two events mutually exclusive or not? 2. Looking at jeeps, P(4WD or big tires) Ask yourself: Can a jeep be both 4WD and have big tires at the same time? Yeah! NOT Mutually Exclusive

Practice Problems 1. A box contains 20 red, 10 blue and 30 yellow beads. What is the probability of a bead drawn at random being: a) red or blue? b) yellow or blue? c) red, blue or yellow? 30/60 = 1/2 40/60 = 2/3 60/60 = 1

Practice Problems 2. The letters of the words ‘HELLO’ and ‘THERE’ are written on individual cards and the cards placed into a bag. A card is picked at random. What is the probability of picking: a) the letter ‘L’ b) the letter ‘E’ c) the letter ‘L’ or ‘E’ d) a consonant e) the letter ‘E’ or a consonant f) the letter ‘L’, ‘E’ or ‘T’ 2/10 = 1/5 3/10 5/10 = 1/2 6/10 = 3/5 9/10 6/10 = 3/5

Practice Problems 3. A set of cards with a letter on each card as shown below are placed into a bag. Howard picks a card at random from the bag. U E A R Q H C H L A Determine the probability that the card is: a) an E. b) not an E. c) not a vowel. d) a P. e) not a P. f) either a Q or U or H g) not a Q, U or H. 1/10 9/10 6/10 = 3/5 1 4/10 = 2/5 6/10 = 3/5

Practice Problems 4. A number is chosen at random from a set of whole numbers from 1 to 50. Calculate the probability that the chosen number: a) is not less than 45 b) is not a multiple of 4 c) is more than 45 d) is not more than 45 6/50 = 3/25 38/50 = 19/25 5/50 = 1/10 45/50 = 9/10

Practice Problems 5. You have a bag with 10 clear marbles numbered 1-10, 10 brown marbles numbered 1-10 and 10 pink marbles numbered 1-10. Find the probability that the chosen number: a) is a 7 or a clear marble b) is an even number or a pink marble c) is a brown marble or a number greater than 8 d) is a number greater than 10 or a pink marble e) a pink marble or a clear marble f) a number greater than 7 or a number less than 3 12/30 = 2/5 14/30 = 7/15 20/30 = 2/3 20/30 = 2/3 10/30 = 1/3 15/30 = 1/2

Find two events A and B that are mutually exclusive Find two events A and B that are mutually exclusive. (Ex: Rolling a die, P(even or odd) -Write down the sample space (Ex: S = {1, 2, 3, 4, 5, 6}) -Write down the set for each event (Ex: Even: {2, 4, 6} Odd: {1, 3, 5}) -Draw a Venn Diagram for the mutually exclusive events -Write the equation for and find the P(A or B) 2. Find two events A and B that are not mutually exclusive. -Write down the sample space -Write down the set for each event -Draw a Venn Diagram for the not mutually exclusive events

3. Find the probability of an event E -Write down the sample space -Write down the set of the event E -Draw a Venn diagram with the set of events inside the circle and outcomes in the sample space that are not in the event outside of the circle -Find the probability of the complement [P(E’)] -Find the P(E) + P(E’) 4. Poll the people in the room about a topic with at least 3 possible choices -Write down each of the choices as well as the frequency for each. -Find the probability of each choice from your collected data. -What type of probability is this?

5. Draw a tree diagram with the different “levels” or events and write down the sample space 6. Create a scenario that uses classical probability 7. Create a scenario that uses empirical probability 8. Create a scenario that uses subjective probability