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**3 Types of Probabilities**

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**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) =

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**3 Types of Probabilities 2. Empirical Probability**

Relies on actual experience to determine the likelihood of outcomes _f_ n P(E) =

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**3 Types of Probabilities Classical Probability & Empirical Probability**

Difference between Classical Probability & Empirical Probability Classical probability assumes that certain outcomes are equally likely

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**3 Types of Probabilities 3. Subjective Probability**

Probability based on an educated guess or estimate I think…

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**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) _

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**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’)

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**What is Mutually Exclusive?**

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

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**are Mutually Exclusive?**

Which of the following are Mutually Exclusive?

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**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

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**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

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**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

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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

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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

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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

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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

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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 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

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**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

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**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?

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**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

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