Pearson Unit 6 Topic 15: Probability 15-1: Experimental and Theoretical Probability Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007

TEKS Focus: (13)(C) Identify whether two events are independent and compute the probability of the two events occurring together with or without replacement. (1)(E) Create and use representations to organize, record, and communicate mathematical ideas. (1)(D) Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

PROBABILITY

Remember that in probability, the set of all possible outcomes of an experiment is called the sample space. Any set of outcomes is called an event. If every outcome in the sample space is equally likely, the theoretical probability of an event is Experimental probability is the actual results from the experiment.

Remember that probability is based on 100%, so in decimal form that is the number 1 (move decimal 2 places to the left to change % to a decimal). Move the decimal 2 places to the right to change a decimal to a %. So the probability of an event NOT occurring is 1 - prob. event occurs.

Example 1: A Quality Control Inspector checks 500 LCD monitors for defects. He finds 3 defective monitors. What is the experimental probability that a monitor inspected at random will have a defect? 3/500 = 0.006 = 0.6%

Example 2: Los Alamos Park has 538 trees. You choose 40 at random and determine that 25 are oak trees. What is the experimental probability that if you chose a tree at random it will be an oak tree? About how many oak trees are in Los Alamos Park? 25 = 0.625 = 62.5% 40 25 = x or (0.625) (538) 538 x = 336.25 About 336 trees will be oak trees.

Result of rolling two dice

Example 3: Suppose you roll two dice (see previous slide). What is the theoretical probability that you will get: Sum of 7 Sum less than 5 The complement of rolling an 11 Sum of 1 6/36 = 1/6 6/36 = 1/6 1 - 2/36 = 36/36 - 2/36 = 34/36 = 17/18 0; there are no possibilities

Example 4: A jar contains 10 red marbles, 8 green marbles, 5 blue marbles and 6 yellow marbles. What is the probability that a randomly selected marble is not green? The jar contains 29 marbles. 29 – 8 green marbles = 21. 21/29

Example 5: Use the spinner below to find the following probabilities: P(even number) = P(a number less than 7) = 4/8 = ½ 6/8 = 3/4

Example 6: 1/3  12 = 4 green marbles 1/2  12 = 6 blue marbles A bag contains 12 marbles. Each marble is green, blue, or red. The probability that a randomly selected marble is green is 1/3 . The probability that a randomly selected marble is blue is ½. How many marbles in the bag are green? Blue? Red? 1/3  12 = 4 green marbles 1/2  12 = 6 blue marbles 12 – 4 – 6 = 2 red marbles