Basic Concepts of ProbabilityUnit 8 - Lesson 2

Key Terms

Probability Experiment - an action, or trial, through which specific results are obtained.

Example: rolling a die (or two dice)

Outcome - result of a single trial

Example: the number showing after a die roll, or the sum of the two faces after two dice are rolled

Sample Space - The set of all possible outcomes - only possible to LIST this if these are discrete outcomes

Example: all the possible rolls of a single die, all possible sums of two dice

Event - a subset of the sample space - can be a collection of more than one outcome

Example: Rolling an even number on a single die {2, 4, 6} or a sum of 5 on two dice { 1,4; 4,1; 2,3; 3,2}

Simple Event - an event that consists of only one outcome

1. The number of outcomes in the sample space gives us the denominator of the theoretical probability.

2. It helps us determine how many outcomes in our sample space are in the subset for a particular event.

Why do we need the sample space?

Last class we determined the sample space for the sum of the faces of two dice to be {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. However, we used a grid/matrix to determine the exact ways each of these could occur in order to determine probabilities (since each outcome wasn't equally likely).

Often just generating the sample space isn't enough - we need to have a way of determining all the possible ways a particular outcome can occur in a sample space so that our probability calculations are accurate.

A tree diagram can be helpful when there are more than 2 things going on in our probability experiment - like rolling 3 dice.

Example 1: Determine the number of outcomes and identify the sample space by using a tree diagram.

a) A probability experiment consists of recording a response to the survey statement at the left and the gender of the respondent

Survey

Does your favoriteteam's win or lossaffect your mood?

Circle one:

Yes

No

Not sure

b) Assuming both genders are equally likely and all responses on the survey are equally likely, what is the probability of getting a boy who responds yes?

When identifying the sample space make sure all letters used are labeled (or make sense).

Example: Let M = Male, F = Female, Y = Yes, N = No, etc.

Create tree diagrams for the following probability experiments:

Creating a sandwich with 2 types of bread - white or rye, 3 types of meat - turkey, ham, or roast beef, and 2 types of cheese - swiss or provolone.

Flipping a coin, then rolling a die.

How large was the sample space in each case?

Do you noticed a pattern?

Two coins are flipped and we are interested in the number of heads and the number of tails:

a) List the sample space (consider a grid/matrix or tree diagram)

b) What is the probability of 2 tails?

c) What is the probability of 1 head and 1 tail?

d) What is the probability of 2 heads?

Suppose a family has four children. When each child is born, assume whether they have a boy or girl is equally likely. We are interested in the number of boys and girls the family has.

a) Create a tree diagram to determine the sample space for this experiment.

b) What is the probability that the family has exactly 1 girl?

c) What is the probability that the family has 2 girls and 2 boys?

d) What is the probability that the family as 3 or more boys?

Exit Ticket

Homework/Classwork: p. 138 #s 2, 18, 19, 23, 24, 41, 43, 45 a&b , 47 - 50, 65