Review Homework

Tree Diagram Worksheet

Roll DICE!!!!

Complete the theoretical probability side of the worksheet.

Roll DICE!!!!

• Experimental Probability

• Roll the dice 100 times – keep track of the outcome using a frequency table:

Roll Tally Frequency

2 |||| | 6

3 |||| |||| 10

4 |||| |||| |||| |||| 19

Karen and Jason roll two dice 50 times and record their results in the accompanying chart.1.)  What is their experimental probability of rolling a 7?2.)  What is the theoretical probability of rolling a 7?3.)  How do the experimental and theoretical probabilities compare?

Solution:  1.)  experimental probability is 13/50 = 26%.2.)  Theoretical probability (based upon what is possible when working with two dice) = 6/36 = 1/6 = 16.7%  (check out the table at the right of possible sums when rolling two dice). 3.)  Karen and Jason rolled more 7's than would be expected theoretically.

Comparing Experimental and Theoretical Probabilities:

Sum of the rolls of two dice

3, 5, 5, 4, 6, 7, 7, 5, 9, 10, 12, 9, 6, 5, 7, 8,  7, 4, 11, 6, 8, 8, 10, 6, 7, 4, 4, 5, 7, 9, 9, 7, 8, 11, 6, 5, 4, 7, 7, 4,3, 6, 7, 7, 7, 8, 6, 7, 8, 9 

The Complementation Rule

For any event E,

P(E) = 1 – P (~ E).

In words, the probability that an event occurs equals 1 minus the probability that it does not occur.

The Special Multiplication Rule (for independent events)

Combinations of Events

The Multiplication Rule – “And”

• The special multiplication rule (for independent events)

• The general multiplication rule (for non-independent events)

The Addition Rule – “Or”

• The special addition rule (mutually exclusive events)

• The general addition rule (non-mutually exclusive events)

When two events, A and B, are mutually exclusive, the probability that A or B will occur is the sum of the

probability of each event.P(A or B) = P(A) + P(B)

Experiment 1:  

A single 6-sided die is rolled. What is the probability of rolling a 2 or a 5?

Possibilities:  

1.  The number rolled can be a 2.

2.  The number rolled can be a 5.

Events:  

These events are mutually exclusive since they cannot occur at the same time.

Addition Rule

Addition Rule 2:  When two events, A and B, are non-mutually exclusive,

the probability that A or B will occur is: P(A or B) = P(A) + P(B) - P(A and B)

In a math class of 30 students, 17 are boys and 13 are girls. On a unit test, 4 boys and 5 girls made an A grade. If a student is chosen at random from the class, what is the probability of choosing a girl or an A student?

P(girl or A)   =  P(girl)  + P(A)  - P(girl and A)

   =  1330

 +   9 30

 -   5 30

 =  1730

Homework

Pages 120, 121, 122#1-7