Aim #10-7: How do we compute probability? Empirical probability applies to situations in which we observe how frequently an event occurs.

Example 1: Using Real-World Data

Check for Understanding:

What is Theoretical Probability? Sample Space is the set of all possible outcomes of an experiment. Example: The sample space of tossing a cone is heads and tails.

Example 2: Computing Theoretical Probability A die is rolled. Find the probability of getting a number less than 5.

Check for Understanding: A die is rolled. Find the probability of getting a number greater than 4.

Example 2: Computing Theoretical Probability Two ordinary six-sided dice are rolled. What is the probability of getting a sum of 8?

Solution: P(E)= 5/ 36

Example 4: Probability and a Deck of 52 Cards You are dealt one card from a standard 52- card deck. Find the probability of being dealt a heart.

Check for Understanding: If you are dealt one card from a standard 52- card deck, find the probability of being dealt a king.

Example 5: Probability and Combinations

Solution:

Extension: Now suppose that a person buys 5000 diferent tickets in Florida’s LOTTO. What is the probability of the person winning?

Check for Understanding:

Probability of an Event Not Occurring

Example 6:

Solution:

Check for Understanding:

Or Probability

Example 7: If one card is randomly selected from a deck of cards, what is the probability of selecting a king or a queen?

Check for Understanding: If you roll a single, six-sided die, what is the probability of getting a 4 or 5?

Or Probability

Example 8:

Check for Understanding: Using the spinner on the right, find the probability that the pointer will stop on an odd number or a number less than 5.

And Probability with Independent Events

Example 10: Independent Events

Solution:

Check for Understanding: Find the probability of green occurring on two consecutive plays on a roulette wheel.

Example 11: Independent Events The picture on the left shows a family that has had nine girls in a row. Find the probability of this occurrence.

Check for Understanding: Find the probability of a family having four boys in a row.

Summary: Answer incomplete sentences. Explain the difference between theoretical and empirical probability. Explain the difference between “or” and “and” probability events. You have a pair of dice. What is the probability of getting a sum of 11.