Probability Sections 12.1, 12.2, 12 - Hampden-Sydney...

ProbabilitySections 12.1, 12.2, 12.3

Lecture 21

Robb T. Koether

Hampden-Sydney College

Fri, Feb 19, 2016

Robb T. Koether (Hampden-Sydney College) ProbabilitySections 12.1, 12.2, 12.3 Fri, Feb 19, 2016 1 / 15

Outline

1 Probability

2 The Probability Model

3 Assignment

Outline

1 Probability

3 Assignment

Probability

The “probability” that a fair coin lands head is 12 .

What exactly does that mean?

If I toss the coin 10 times, I will get 5 heads?

That is simply not true.

If I toss the coin many times, I will get heads “about” half the time?

Then shouldn’t we say that the probability is “about” 12 , not “exactly”

Probability

What exactly does that mean?If I toss the coin 10 times, I will get 5 heads?

That is simply not true.If I toss the coin many times, I will get heads “about” half the time?

Probability

That is simply not true.

If I toss the coin many times, I will get heads “about” half the time?

Probability

Definition (Probability)The probability of a particular outcome of procedure is the proportionof the times that that outcome occurs out an enormous number(actually infinite number) of repetitions of the procedure.

More technically, it is the “limit” of the proportion of the time thatthe outcome occurs.That means that the proportion of times that the particularoutcome actually occurs will get closer and closer to the exactvalue as the number of repetitions increases.

Outline

1 Probability

3 Assignment

The Probability Model

The basis of a probability model is a procedure.The procedure involves at least one step that is left to chance.When we perform the procedure, we observe a specific outcome.

Example

Example (Probability Model)In the coin-tossing example,

The procedure is to toss the coin.The outcome that we observe is which side landed up.

The Probability Model

Definition (Sample Space)The sample space of a procedure is the set of all possible outcomes.

Definition (Event)An event is a set of outcomes. That is, it is a subset of the samplespace.

Example

Example (Tossing a Coin)Let the procedure be to toss a coin.The observation is, which side landed up.The possible outcomes are heads (H) and tails (T).

What is the sample space?List a couple of events.

Example

Example (Tossing a Coin)Let the procedure be to toss a coin.The observation is, which side landed up.The possible outcomes are heads (H) and tails (T).What is the sample space?

List a couple of events.

Example

Example (Tossing a Coin)Let the procedure be to toss a coin.The observation is, which side landed up.The possible outcomes are heads (H) and tails (T).What is the sample space?List a couple of events.

Example

Example (Rolling a Die)Let the procedure be to roll a die.The observation is, which number landed up.

What is the sample space?List a couple of events.Describe the event “the number is odd.”

Example

Example (Rolling a Die)Let the procedure be to roll a die.The observation is, which number landed up.What is the sample space?

List a couple of events.Describe the event “the number is odd.”

Example

Example (Rolling a Die)Let the procedure be to roll a die.The observation is, which number landed up.What is the sample space?List a couple of events.

Describe the event “the number is odd.”

Example

Example (Rolling a Die)Let the procedure be to roll a die.The observation is, which number landed up.What is the sample space?List a couple of events.Describe the event “the number is odd.”

Example

Example (Rolling a Pair of Dice)Let the procedure be to roll a pair of dice.The observation is, which number landed up on each die.

What is the sample space?List a couple of events.Describe the event “the sum of the two numbers is 7.”

Example

Example (Rolling a Pair of Dice)Let the procedure be to roll a pair of dice.The observation is, which number landed up on each die.What is the sample space?

List a couple of events.Describe the event “the sum of the two numbers is 7.”

Example

Example (Rolling a Pair of Dice)Let the procedure be to roll a pair of dice.The observation is, which number landed up on each die.What is the sample space?List a couple of events.

Describe the event “the sum of the two numbers is 7.”

Example

Example (Rolling a Pair of Dice)Let the procedure be to roll a pair of dice.The observation is, which number landed up on each die.What is the sample space?List a couple of events.Describe the event “the sum of the two numbers is 7.”

Example

Example (Rolling a Pair of Dice)Let the procedure be to roll a pair of dice.The observation is the sum of the two numbers.

What is the sample space?List a couple of events.Describe the event “the sum of the two numbers is 7.”

Example

Example (Rolling a Pair of Dice)Let the procedure be to roll a pair of dice.The observation is the sum of the two numbers.What is the sample space?

List a couple of events.Describe the event “the sum of the two numbers is 7.”

Example

Example (Rolling a Pair of Dice)Let the procedure be to roll a pair of dice.The observation is the sum of the two numbers.What is the sample space?List a couple of events.

Describe the event “the sum of the two numbers is 7.”

Example

Example (Rolling a Pair of Dice)Let the procedure be to roll a pair of dice.The observation is the sum of the two numbers.What is the sample space?List a couple of events.Describe the event “the sum of the two numbers is 7.”

Outline

1 Probability

3 Assignment

Assignment

AssignmentRead Sections 12.1, 12.2, 12.3.Apply Your Knowledge: 5, 6, 7.Check Your Skills: 22, 23, 25, 26, 27.Exercises 32, 33, 35, 36, 38.

Probability Sections 12.1, 12.2, 12 - Hampden-Sydney...

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