In the previous sections, you examined ways to determine the probability of simple events and independent events. In this section, you will use data to make predictions from the probability of one or more events.

Sources: Cedar Hill State Park, QuesterMark, Flickr
San Jacinto Monument Star, Tijuana Brass, Wikimedia Commons
Big Tree, Larry D. Moore, Wikimedia Commons
Mustang State Park Nima, Zereshk, Wikimedia Commons
Garnerview3, Baylordad, Wikimedia Commons

A recent survey of Texas state park users revealed the five most popular state parks. The results are shown in the table below.

Use the data in the table to answer the following questions.

• Based on this data, what is the probability that the next state park user randomly surveyed will say that Garner State Park is their favorite?

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  Probability is the ratio of the desired outcomes to the total number of possible outcomes. Use the data in the table to set up a probability ratio.
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  There are 40 total respondents.
  
  P(Garner) = number of respondents for Garner over total number of respondents Number of Respondents for Garner Total Number of Respondents = 6 over 40 6 40 = 6÷2 over 40÷2 6 ÷ 2 40 ÷ 2 = 3 over 20 3 20
• Based on this data, what is the probability that the next state park user randomly surveyed will say that either Goose or Mustang Island is their favorite?

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  Probability is the ratio of the desired outcomes to the total number of possible outcomes. Use the data in the table to set up a probability ratio. This situation describes only one event, since only one person is being surveyed. Determine the sum of the probabilities of a person either responding “Goose Island” or “Mustang Island.”
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  P(Goose Island) = number of respondents for Garner over total number of respondents Number of Respondents for Goose Island Total Number of Respondents = 8 over 40 8 40
  
  P(Mustang Island) = number of respondents for Garner over total number of respondents Number of Respondents for Mustang Island Total Number of Respondents = 7 over 40 7 40
  
  P(Goose Island or Mustang Island) = P(Goose Island) + P(Mustang Island)
  
  P(Goose Island or Mustang Island) = 8 over 40 8 40 + 7 over 40 7 40 = 15 over 40 15 40 = 15÷5 over 40÷5 15 ÷ 5 40 ÷ 5 = 3 over 8 3 8
• Based on the data, what is the probability that the next two state park users randomly surveyed will say that Cedar Hill State Park is their favorite?

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  Probability is the ratio of the desired outcomes to the total number of possible outcomes. Use the data in the table to set up a probability ratio. These are also independent events, since the likelihood that the second person will say “Cedar Hill State Park” does not depend on whether or not the first person does.
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  P(Cedar Hill and Cedar Hill) = P(Cedar Hill) × P(Cedar Hill)
  
  P(Cedar Hill) = number of respondents for Cedar Hill over total number of respondents Number of Respondents for Cedar Hill Total Number of Respondents = 11 over 40 11 40
  
  P(Cedar Hill and Cedar Hill) = 11 over 40 11 40 × 11 over 40 11 40 = 121 over 1600 121 1600
• Anessa decides to survey 200 people to determine which of the five state parks they prefer. Based on the information in the table, how many people should Anessa expect to say that the San Jacinto Monument and Battleground is their favorite state park?

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  Use the data in the table to set up and solve a proportion.
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  Anessa should expect 40 out of 200 people to prefer the San Jacinto Monument and Battleground.

Pause and Reflect

How can you use data to determine the probability that an event will occur?

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Use the data to determine the number of desired outcomes and the total number of possible outcomes.

Practice

Majida surveyed 30 of her classmates to determine which sport was their favorite. Her results are shown in the table below. Use this information to answer questions 1 – 3.

1. Based on this data, if Majida randomly surveyed one more person, what is the probability the person would prefer basketball?

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   Use the data to determine the number of desired outcomes (number of students who prefer basketball) and the total number of outcomes.
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   P(basketball) = number for basketball over total number of respondents Number for Basketball Total Number of Respondents = 10 over 30 10 30 = 10÷10 over 30÷10 10 ÷ 10 30 ÷ 10 = 1 over 3 1 3
2. Based on the data, what is the probability that the next two people surveyed would prefer volleyball or basketball?

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   Use the data to determine the number of desired outcomes (number of students who prefer volleyball or basketball) and the total number of outcomes. If Majida surveys two people, the results are independent events since the second person’s response is not dependent on the first person’s response.
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   P(volleyball or basketball AND volleyball or basketball) = P(volleyball or basketball) × P(volleyball or basketball)
   
   P(volleyball or basketball) = number for volleyball or basketball over total number of respondents Number for Volleyball or Basketball Total Number of Respondents
   
   P(volleyball or basketball) = 5 + 10 over 30 5 + 10 30 = 15 ocwe 30 15 30 = 15÷15 over 30÷15 15 ÷ 15 30 ÷ 15 = 1 over 2 1 2
   
   P(volleyball or basketball AND volleyball or basketball) = 1 over 2 1 2 × 1 over 2 1 2 = 1 over 4 1 4
3. Jake wants to survey 120 students in the cafeteria to determine their favorite sport. If his results are similar to Majida’s survey results, how many people should he expect to say that football is their favorite sport?

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   Use the data to set up and solve a proportion.
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