1. Section 4-5 Probability SPI 53B: compute the probability of a simple compound event Objectives: Find theoretical and experimental probability Collect and analyze data for probability Probability: how likely something will occur (the probability that it will rain today) Outcome: results of a single trial, like one roll of a number cube Event: any outcome or group of outcomes

2. Sample space: all possible outcomes Complement of an event: all outcomes not in the event Theoretical probability: based on possible outcomes that are equally likely to occur Experimental probability: outcomes based on data collected

3. The probability of an event ranges from 0 to 1, so it will be written as a fraction, decimal, or a percent. less likely more likely 0 0.5 1 Probability of an Event Impossible event Roll a 7 on a number cube Equally likely or unlikely Certain to occur Land heads or tails on a coin Roll a number less than 7 on a number cube

4. EVENTSAMPLE SPACE FAVORABLE OUTCOMES Apply Vocabulary Find the probability of rolling an even number using a number cube. Roll an even number 1, 2, 3, 4, 5, 6 2, 4, 6

5. Complement of an Event Possible outcomes of Rolling a number cube Outcomes for rolling An even number Complement of rolling An even number 1, 2, 3, 4, 5, 6 2, 4, 6 1, 3, 5 P(event) + P(not event) = 1 -------- or ---------- P (not event) = 1 – P(event) Complement of an event consists of all outcomes NOT in the event. The probability of an event and its complement (not an event) will always equal 1.

6. A bowl contains 12 slips of paper, each with a different name of the month. Find the theoretical probability that a slip selected at random has a name of the month that starts with J. Sample Space: { J F M A M J J A S O N D } Finding Probability Find the complement of the event:

7. Experimental Probability: based on data collected from repeated trials P(event) = number of times an event occurs number of times the experiment is done Experimental vs Theoretical Probability

8. Experimental Probability 500 belts were inspected at random. They found no defects in 485 belts. What is the probability that a belt selected at random will pass quality control? P(no defects) = number of times an event occurs number of times the experiment is done The probability that a belt has no defects is 97%. = Substitute. 485 500 = 0.97 = 97% Simplify. Write as a percent.

9. If the belt manufacturer has 6258 belts, predict how many belts are likely to have no defects. Use the.97 (no defects) from previous example. number with no defects = P(no defects) number of belts = 0.97 6258 Substitute. Use 0.97 for 97%. = 6070.26 Simplify. Approximately 6070 belts are likely to have no defects. Probability

10. How does experimental probability of rolling a number cube and throwing a 2 compare to theoretical probability? Theoretical: P(rolling a 2) = ______ Experimental: Make a chart of the results 1. P(roll 2 after 10 rolls) = 2. P(roll 2 after 20 rolls) = 3. P(roll 2 after 30 rolls) = # of number cube rolls 102030 # cube lands on 2 * The more times you roll the cube, the closer experimental should be to theoretical. Rolling a Number Cube (Group of Two)