Experimental Probability 11-2 Experimental Probability Course 1 Warm Up Problem of the Day Lesson Presentation

Experimental Probability Course 1 11-2 Experimental Probability Warm Up Write impossible, unlikely, equally likely, likely, or certain to describe each event. 1. A particular person’s birthday falls on the first of a month. 2. You roll an odd number on a fair number cube. 3. There is a 0.14 probability of picking the winning ticket. Write this as a fraction and as a percent. unlikely equally likely , 14% 7 50 __

Experimental Probability Course 1 11-2 Experimental Probability Problem of the Day Max picks a letter out of this problem at random. What is the probability that the letter is in the first half of the alphabet? 57 101 ___

Today’s Learning Goal Assignment Course 1 11-2 Experimental Probability Today’s Learning Goal Assignment Learn to find the experimental probability of an event.

Insert Lesson Title Here Course 1 11-2 Experimental Probability Insert Lesson Title Here Vocabulary experiment outcome sample space experimental probability

Experimental Probability Course 1 11-2 Experimental Probability An experiment is an activity involving chance that can have different results. Flipping a coin and rolling a number cube are examples of experiments. The different results that can occur are called outcomes of the experiment. If you are flipping a coin, heads is one possible outcome. The sample space of an experiment is the set of all possible outcomes. You can use {} to show sample spaces. When a coin is being flipped, {heads, tails} is the sample space.

Additional Example 1A: Identifying Outcomes and Sample Spaces Course 1 11-2 Experimental Probability Additional Example 1A: Identifying Outcomes and Sample Spaces For each experiment, identify the outcome shown and the sample space. A. Spinning two spinners outcome shown: B1 sample space: {A1, A2, B1, B2}

Experimental Probability Course 1 11-2 Experimental Probability Try This: Example 1A For each experiment, identify the outcome shown and the sample space. A. Spinning two spinners C D 3 4 outcome shown: C3 sample space: {C3, C4, D3, D4}

Additional Example 1B: Identifying Outcomes and Sample Spaces Course 1 11-2 Experimental Probability Additional Example 1B: Identifying Outcomes and Sample Spaces For each experiment, identify the outcome shown and the sample space. B. Spinning a spinner outcome shown: green sample space: {red, purple, green}

Experimental Probability Course 1 11-2 Experimental Probability Try This: Example 1B For each experiment, identify the outcome shown and the sample space. B. Spinning a spinner outcome shown: blue sample space: {blue, orange, green}

Experimental Probability Course 1 11-2 Experimental Probability Performing an experiment is one way to estimate the probability of an event. If an experiment is repeated many times, the experimental probability of an event is the ratio of the number of times the event occurs to the total number of times the experiment is performed.

Experimental Probability Course 1 11-2 Experimental Probability Writing Math The probability of an event can be written as P(event). P(blue) means “the probability that blue will be the outcome.”

Additional Example 2: Finding Experimental Probability Course 1 11-2 Experimental Probability Additional Example 2: Finding Experimental Probability For one month, Mr. Crowe recorded the time at which his train arrived. He organized his results in a frequency table. Time 6:49-6:52 6:53-6:56 6:57-7:00 Frequency 7 8 5

Additional Example 2A Continued Course 1 11-2 Experimental Probability Additional Example 2A Continued A. Find the experimental probability that the train will arrive before 6:57. Before 6:57 includes 6:49-6:52 and 6:53-6:56. P(before 6:57)  number of times the event occurs total number of trials ___________________________ = 7 + 8 20 _____ = 15 20 ___ = 3 4 __

Additional Example 2B: Finding Experimental Probability Course 1 11-2 Experimental Probability Additional Example 2B: Finding Experimental Probability B. Find the experimental probability that the train will arrive between 6:53 and 6:56. P(between 6:53 and 6:56)  number of times the event occurs total number of trials ___________________________ = 8 20 ___ = 2 5 __

Experimental Probability Course 1 11-2 Experimental Probability Try This: Example 2 For one month, Ms. Simons recorded the time at which her bus arrived. She organized her results in a frequency table. Time 4:31-4:40 4:41-4:50 4:51-5:00 Frequency 4 8 12

Experimental Probability Course 1 11-2 Experimental Probability Try This: Example 2A A. Find the experimental probability that the bus will arrive before 4:51. Before 4:51 includes 4:31-4:40 and 4:41-4:50. P(before 4:51)  number of times the event occurs total number of trials ___________________________ = 4 + 8 24 _____ = 12 24 ___ = 1 2 __

Experimental Probability Course 1 11-2 Experimental Probability Try This: Example 2B B. Find the experimental probability that the bus will arrive between 4:41 and 4:50. P(between 4:41 and 4:50)  number of times the event occurs total number of trials ___________________________ = 8 24 ___ = 1 3 __

Additional Example 3: Comparing Experimental Probabilities Course 1 11-2 Experimental Probability Additional Example 3: Comparing Experimental Probabilities Erika tossed a cylinder 30 times and recorded whether it landed on one of its bases or on its side. Based on Erika’s experiment, which way is the cylinder more likely to land? Outcome On a base On its side Frequency llll llll llll llll llll llll l Find the experimental probability of each outcome.

Additional Example 3 Continued Course 1 11-2 Experimental Probability Additional Example 3 Continued = 9 30 ___ P(base)  number of times the event occurs total number of trials ___________________________ = 21 30 ___ P(side)  number of times the event occurs total number of trials ___________________________ 9 30 ___ < 21 30 ___ Compare the probabilities. It is more likely that the cylinder will land on its side.

Additional Example 3: Comparing Experimental Probabilities Course 1 11-2 Experimental Probability Additional Example 3: Comparing Experimental Probabilities Chad tossed a cylinder 25 times and recorded whether it landed on one of its bases or on its side. Based on Chads’s experiment, which way is the cylinder more likely to land? Outcome On a base On its side Frequency llll llll llll llll llll Find the experimental probability of each outcome.

Try This: Example 3 Continued Course 1 11-2 Experimental Probability Try This: Example 3 Continued = 5 25 ___ P(base)  number of times the event occurs total number of trials ___________________________ = 20 25 ___ P(side)  number of times the event occurs total number of trials ___________________________ 5 25 ___ < 20 25 ___ Compare the probabilities. It is more likely that the cylinder will land on its side.

Experimental Probability Insert Lesson Title Here Course 1 11-2 Experimental Probability Insert Lesson Title Here Lesson Quiz: Part 1 1. The spinner below was spun. Identify the outcome shown and the sample space. outcome: green; sample space: {red, blue, green, purple, yellow}

Experimental Probability Insert Lesson Title Here Course 1 11-2 Experimental Probability Insert Lesson Title Here Lesson Quiz: Part 2 Sandra spun the spinner above several times and recorded the results in the table. 2. Find the experimental probability that the spinner will land on blue. 3. Find the experimental probability that the spinner will land on red. 4. Based on the experiment, on which color will the spinner most likely land? 2 9 __ 4 9 __ red