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7.8 Simple Probability

7.8 Simple Probability. An outcome is a possible result. An event is a specific outcome. A favorable event is the outcome you’re looking for. Random means all outcomes are equally likely to occur or happen. random = fair.

candace-roberson
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7.8 Simple Probability

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  1. 7.8 Simple Probability

  2. An outcome is a possible result • An event is a specific outcome • A favorable event is the outcome you’re looking for • Random means all outcomes are equally likely to occur or happen. • random = fair

  3. The probability that an event will happen is a number between 0 and 1: A probability of 0 means the event will definitely NOT happen. A probability of 1 means the event definitely WILL happen. All other probabilities are between 0 and 1

  4. Probability 0 Impossible 1 Definite 50-50 chance The probability that an event will happen can be also described as a percent. 0 Impossible 50% 100% Definite

  5. Probability is the chance that some event will happen. It can be written as a ratio. # of favorable outcomes (what you want) total # of possible outcomes

  6. There are 2 types of probabilities: 1) Theoretical 2) Experimental • Theoretical probability is calculated. • # of favorable outcomes # of possible outcomes • Experimental probability is based on actual results (something you did and counted).

  7. Now turn to page 383 and try Guided Practice problems 1 and 2

  8. Guided Practice problem 1 You roll a number cube (dice) 100 times. Your results are given in the table below. What is the experimental probability of rolling a number greater than 3? Remember, experimental probability is based on something that you actually did! So use the numbers in the chart. Probability = number of favorable outcomes number of total outcomes P = 16 + 14 + 18________ 17 + 15 + 20 + 16 + 14 + 18 P =

  9. Guided Practice problem 1 continued You roll a number cube (dice) 100 times. Your results are given in the table below. What is the theoretical probability of rolling a number greater than 3? • Remember, theoretical probability is based the possible outcomes. Probability = number of favorable outcomes number of total outcomes P =

  10. Guided Practice problem 1 continued You roll a number cube (dice) 100 times. Your results are given in the table below. So the experimental probability of rolling a number greater than 3 was 48% based on the experiment that was done. • Theoretical probability or calculated probability was 50%. The experimental probability becomes more accurate or closer to the theoretical probability when there are more trials.

  11. Guided Practice problem 2 Use the information in Example 3. About how many buttons would you expect to be defective in a shipment of 25,000 buttons? A company manufactures buttons. A quality control inspector finds 2 defective buttons in a batch of 300 buttons. About how many buttons would you expect to be defective in a shipment of 25,000 buttons? Use cross products to find the answer. 300x = 50,000 divide both sides by 300 x = 166 About 167 buttons

  12. Probability of Compound Events Independent Events – events that do not effect each other To calculate the probability of 2 independent events: Find the probability of each one, then multiply Ex. What is the probability of rolling a 1 and then rolling a 2 on a standard die. P(1) = P(2)= P(1 then 2)=

  13. Let’s try some: • Suppose you roll a red die and a blue die. What is the probability that you will roll a 5 on the red and a 1 or 2 on the blue. The probability of rolling a 5 is The probability of rolling a 1 or a 2 is To find the probability of BOTH, multiply them: The probability that you will roll a 5 on the red and a 1 or 2 on the blue is r 5.6%

  14. There is a bag of marbles. There are 4 white, 3 black, 8 purple, 2 red, and 8 green. • Find the probability of choosing a purple, then a red after replacing the 1st marble. • The probability of choosing a purple marble first is since there are 8 purple marbles out of 25 total marbles. Since I am replacing the purple one after I picked it, the probability of picking a red marble next is because there are 2 red marbles out of 25 total. • To find the probability of picking a purple and then a red, you multiply the two probabilities together. • * = or about 2.6%

  15. There is a bag of marbles. There are 4 white, 3 black, 8 purple, 2 red, and 8 green. • Find the probability of choosing a purple, then a red withoutreplacing the 1st marble. • The probability of choosing a purple marble first is since there are 8 purple marbles out of 25 total marbles. Since I am NOT replacing the purple one after I picked it, the probability of picking a red marble next is because there are 2 red marbles out of 24 total. • To find the probability of picking a purple and then a red, you multiply the two probabilities together. • * = or about 2.7%

  16. Compound probability will NOT be on the test! If you don’t get it, don’t worry…we will talk about it in class. If you are feeling confident about simple probability, you can get a head start on the classwork. Pages 383 – 385 1-23

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