Math CC7/8 – Jan. 20 Math Notebook: Things Needed Today (TNT): Pencil/Math Notebook/Calculator Math Notebook: Topic: Developing Probability Models 2. HW: WDYE p. 37-42 #4-7, 18 – 25

What’s Happening Today? Warm Up Lesson 2.2 Begin HW?

Write your detailed explanation in your math notebook  Warm Up Using your own words, explain the difference between theoretical and experimental probability. Write your detailed explanation in your math notebook 

Experimental vs. Theoretical Probability We are going to do a class experiment, record your data, and compare experimental to theoretical probabilities . A bag contains 6 yellow blocks, 3 blue blocks, and 9 red blocks. You choose from the bag at random. Choose 10 times. How do your experimental probabilities compare to your theoretical probabilities?

Rolling a Dice/Number Cube “or” What is the probability that 1 “or” 6 will occur when you roll a 6- sided number cube? P(1 or 6) = P(1) + P(6) = 1/6 + 1/6 = 2/6 or 1/3 “and” What is the probability that the number is greater than 3 “and” even? (Must be both) P(>3 and even) = P(4 or 6) = P(4) + P(6) ‘OR’ ‘AND’

Rolling a Dice/Number Cube What is the probability of rolling a number that is “not” even? P(not even) = P(1 or 3 or 5) = 1/6 + 1/6 + 1/6 = 3/6 or ½ P(not even) = 1 – P(even) = 1 – 3/6 = ½ *Complement*

What are some properties of theoretical probabilities? Question What are some properties of theoretical probabilities?

The probability the marble is yellow? 1. What is… The probability the marble is yellow? The probability the marble is blue? The probability the marble is red? 2. What is the sum of the probabilities? P(Y) + P(B) + P(R) = 2/12 + 4/12 + 6/12 = 12/12 = 1 P(Y) = 2/12 P(B) = 4/12 P(R) = 6/12

4. The probability the marble is not blue? P( not B) = 1 – P(B) 3. What color is the selected marble most likely to be? Most likely Red because there are more red marbles. What is… 4. The probability the marble is not blue? P( not B) = 1 – P(B) = 1 – (4/12) = 8/12 5. The probability the marble is either red or yellow? P(R or Y) = P(R) + P(Y) = 6/12 + 2/12 = 8/12 6. The probability the marble is white? P(W) = 0/12 = 0! Impossible!

Review P(A) + P(B) 1 – P(A) P(A or B) = P(not A) = P(A and B) =

Adsila is correct. In general, the number of favorable events can never be greater than the total number of events, so a probability can never be greater than 1 (but it can equal 1).

P(Y) = 2/12 = 4/24 P(B) = 4/12 = 8/24 P(R) = 6/12 = 12/24 No, the probabilities do not change! Each color doubles, and the total doubles. ? Currently 24 marbles, of which 8 are blue. You need 8 more blue marbles so that there will be 16 marbles out of 32 marbles now!

6 marbles is the smallest number that gives a 1/6 probability. P (Blue) = 1 – P (Red + White) = 1 – (1/6 + 1/3) = 1 – (3/6) = 1/2 6 marbles is the smallest number that gives a 1/6 probability. 2 red, 1 white and 3 blue marbles

Yes, the bag could contain 48 marbles. 16 red, 8 white, and 24 blue 12 blue marbles. Blue will equal red plus white.

There is no difference in probabilities if you use marbles or blocks as long as each marble or block is the same size and shape! The more trials you conduct, the closer the experimental probability gets to the theoretical probability.

Homework: WDYE 2.2 p. 37-42 #4-7 #18 – 25