Experimental Probability 12-2 Experimental Probability Course 1 Warm Up Problem of the Day Lesson Presentation

Experimental Probability Course 1 12-2 Experimental Probability Warm Up Write impossible, unlikely, as likely as not, 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 as likely as not , 14% 7 50 __

Experimental Probability Course 1 12-2 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 ___

Experimental Probability Course 1 12-2 Experimental Probability Learn to find the experimental probability of an event.

Insert Lesson Title Here Course 1 12-2 Experimental Probability Insert Lesson Title Here Vocabulary experiment outcome experimental probability

Experimental Probability Course 1 12-2 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.

Additional Example 1A: Identifying Outcomes Course 1 12-2 Experimental Probability Additional Example 1A: Identifying Outcomes For each experiment, identify the outcome shown. tossing two coins outcome shown: tails, heads (T, H)

Experimental Probability Course 1 12-2 Experimental Probability Additional Example 1B: Identifying Outcomes For each experiment, identify the outcome shown. rolling two number cubes outcome shown: (2, 6)

Experimental Probability Course 1 12-2 Experimental Probability Check It Out: Example 1A For each experiment, identify the outcome shown. spinning two spinners C D 3 4 outcome shown: C3

Experimental Probability Course 1 12-2 Experimental Probability Check It Out: Example 1B For each experiment, identify the outcome shown. tossing two coins outcome shown: heads, heads (H, H)

Experimental Probability Course 1 12-2 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 12-2 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 12-2 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 6:50-6:52 6:53-6:56 6:57-7:00 Frequency 7 8 5

Additional Example 2A Continued Course 1 12-2 Experimental Probability Additional Example 2A Continued Find the experimental probability of the train arriving between 6:57 and 7:00. P(between 6:57 and 7:00)  number of times the event occurs total number of trials ___________________________ = 5 20 ___ = 1 4 __

Additional Example 2B: Finding Experimental Probability Course 1 12-2 Experimental Probability Additional Example 2B: Finding Experimental Probability Find the experimental probability of the train arriving before 6:57. Before 6:57 includes 6:50-6:52 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 __

Experimental Probability Course 1 12-2 Experimental Probability Check It Out: 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 12-2 Experimental Probability Check It Out: Example 2A 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 12-2 Experimental Probability Check It Out: Example 2B 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 12-2 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 12-2 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.

Experimental Probability Course 1 12-2 Experimental Probability Check It Out: Example 3 Chad tossed a dome 25 times and recorded whether it landed on its base or on its side. Based on Chad’s experiment, which way is the dome more likely to land? Outcome On its side On its base Frequency llll llll llll llll llll Find the experimental probability of each outcome.

Check It Out: Example 3 Continued Course 1 12-2 Experimental Probability Check It Out: Example 3 Continued = 5 25 ___ P(side)  number of times the event occurs total number of trials ___________________________ = 20 25 ___ P(base)  number of times the event occurs total number of trials ___________________________ 5 25 ___ < 20 25 ___ Compare the probabilities. It is more likely that the dome will land on its base.

Experimental Probability Insert Lesson Title Here Course 1 12-2 Experimental Probability Insert Lesson Title Here Lesson Quiz: Part I 1. The spinner below was spun. Identify the outcome shown. outcome: green

Experimental Probability Insert Lesson Title Here Course 1 12-2 Experimental Probability Insert Lesson Title Here Lesson Quiz: Part II 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, what is the probability that the spinner will land on red or blue? 2 9 __ 4 9 __ 2 3 __