4.2 Basic Probability Rules

4.2 Basic Probability Rules

Learning Targets

• Give a probability model for a chance process with equally likely outcomes and use it to find the probability of an event.

• Use the complement rule to find probabilities.

• Use the addition rule for mutually exclusive events to find probabilities.

Probability Model

• A probability model is a description of some chance process that consists of two parts: a list of all possible outcomes and the probability for each outcome.

• The list of all possible outcomes is called the sample space.

• A probability model allows us to find the probability of an event.

• An event is any collection of outcomes from some chance process.

Example: Probability Model

Imagine rolling two fair, six-sided dice-one that’s red and one that’s blue. How do we develop a probability model for this chance process? Each of these 36 outcomes will be equally likely and have probability 1/36.

Finding probabilities

• Event A: Getting a sum of 5

• P(A) = 4/36 = 0.111

Fill in the Blank

If you flip a coin 2 times, how many possible outcomes are there?

Correct: 4

• HH, HT, TH, TT

Multiple Choice

If you flip a coin 2 times, what's the probability of getting heads exactly one time?

• 1/4

• 2/4

• 3/4

• 4/4

Basic Probability Rules

• The probability of any event is a number between 0 and 1.

• All possible outcomes together must have probabilities that add up to 1.

• The probability that an event does not occur is 1 minus the probability that the event does occur.

Multiple Choice

Is 0.36 a valid probability for an event?

• Yes

• No

Multiple Choice

Is 1.6 a valid probability for an event?

• Yes

• No

Why is this a valid probability model?

• The probability of each outcome is a number between 0 and 1.

• 0.24+0.20+0.16+0.14+0.13+0.13 = 1

Find the probability that you don't get blue?

• P(not blue) =

• 1 - P(blue) =

• 1 - 0.24 =

• 0.76

Fill in the Blank

What is the probability of getting yellow?

Fill in the Blank

What is the probability of NOT getting yellow?

Fill in the Blank

What is the probability of NOT getting orange?

Mutually Exclusive

• Two events A and B are mutually exclusive if they can not happen at the same time. P(A and B) = 0

• The addition rule for mutually exclusive events A and B says that P(A or B) = P(A) + P(B)

2015 AP Statistics

• Find the probability that the chosen student scored less than a 3.

• P(scored less than 3) = P(scored 1 or 2) = P(scored 1) + P(scored 2) = 0.236 + 0.186 = 0.422

2015 AP Statistics

• Find the probability that the chosen student scored earned a passing score. (Passing = 3, 4, or 5)

• P(passing score) = 1 - P(less than 3) = 1 - 0.422 = 0.578

• Also: P(passing) = P(3 or 4 or 5) = P(3)+P(4)+P(5) = 0.252+0.191+0.135=0.578

Fill in the Blank

What is the probability of scoring less than a 5?