Theoretical ProbabilityGoal: to find the probability of an event using theoretical probability.

Probability A probability experiment is an activity in

which results are observed. Each observation is called a trial, and each result is called an outcome. The sample space is the set of all possible outcomes of an experiment.

An Event…

An event is any set of one or more outcomes.

The probability of an event, written P(event), is a number from 0 (or 0%) to 1 (or 100%) that tells you how likely the event is to happen. A probability of 0 means the event is

impossible, or can never happen. A probability of 1 means the event is

certain, or has to happen. The probabilities of all possible outcomes

in the sample space add up to 1.

Theoretical probability Theoretical probability is used to

estimate probabilities by making certain assumptions about an experiment.

The assumption is that all outcomes that are equally likely, that is, they all have the same probability.

To find theoretical probability:number of outcomes in the event

total possible outcomes

Example #1: An experiment consists of rolling a fair

die. There are 6 possible outcomes: 1, 2, 3, 4, 5, and 6.

What is the probability of rolling a 3, P(3)?

What is the probability of rolling an odd number, P(odd number)?

What is the probability of rolling a number less than 5, P(less than 5)?

number of outcomes in the event total possible outcomes

Example #2: An experiment consists of rolling

one fair die and flipping a coin. Show a sample space that has all

outcomes equally likely.

number of outcomes in the event total possible outcomes

What is the probability of getting tails, P(tails)?

What is the probability of getting an even number and heads, P(even # and heads)?

What is the probability of getting a prime number, P(prime)?

1H 2H 3H 4H 5H 6H1T 2T 3T 4T 5T 6T

Example #3:Using the spinner, find

the probability of each event.

P(spinning A)

P(spinning C)

P(spinning D)

Example #4: Suppose you roll two fair

dice and are considering the sum shown.

Since each die represents a unique number, there are 36 total outcomes.

What is the probability of rolling doubles?

There are 6 outcomes of rolling doubles: (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), and (6, 6).

P(double) =

Example #4 cont…. What is the probability

of rolling a total of 10? There are 6 outcomes in the

event “a total of 10”: (4, 6), (5, 5), and (6, 4).

P(total = 10) = What is the probability

that the sum shown is less than 5?

There are 6 outcomes in the event “total < 5” :(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), and (3, 1).

P(total < 5) =

Example #5:

An experiment consists of rolling a single fair die. Find P(rolling an even number)

Find P(rolling a 3 or a 5)

Example #6:

Mrs. Rife has candy hearts in a jar. She has 27 red hearts, 16 pink hearts, and 17 white hearts. What is the theoretical probability of

drawing a white heart?

A red heart?.

Example #7:

Find each probability. P(white)

P(red)

P(green)

P(black)

What should be the sum of the probabilities? Is it true?

Example #8:

Three fair coins are tossed: a penny, a dime, and a quarter. Copy the table and then find the followingP(HHT)P(TTT)P(0 tails)P(1 tail)P(2 heads)P(all the same)

Penny Dime Quarter OutcomeH H H HHHH H T HHTH T H HTHH T T HTTT H H THHT H T THTT T H TTHT T T TTT

Example #7:

Find each probability. P(white)

P(red)

P(green)

P(black)

What should be the sum of the probabilities? Is it true?