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

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

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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

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