Classroom Resource

Using Probability in Search-and-Rescue Operations | Prediction by the Numbers

Subject Area

Mathematics

Grade(s)

8

Overview

Explore how probability can be used to help find people lost at sea, even when rescuers have very little information, in this video from NOVA: Prediction by the Numbers. To improve its search-and-rescue efforts, the U.S. Coast Guard has developed a system that uses Bayesian inference, a mathematical concept that dates back to the 18th century. The Search and Rescue Optimal Planning System (SAROPS) uses a mathematical approach to calculate probabilities of where a floating person or object might be based on changing ocean currents, wind direction, or other new information. Use this resource to stimulate thinking and questions about appropriate uses of statistical methods.

Mathematics (2019) Grade(s): 8 - Grade 8 Accelerated

MA19.8A.44

Explain whether two events, A and B, are independent, using two-way tables or tree diagrams. [Algebra I with Probability, 38]

Unpacked Content

UP:MA19.8A.44

Vocabulary

  • Independent event
  • Probability
  • Dependent event
  • Event
  • Two-way table
  • Tree diagram
  • Simple event
  • Compound event

Knowledge

Students know:
  • Methods to find probability of simple and compound events.

Skills

Students are able to:
  • Interpret the given information in the problem.
  • Accurately determine the probability of simple and compound events.
  • Accurately calculate the product of the probabilities of two events.

Understanding

Students understand that:
  • Events are independent if one occurring does not affect the probability of the other occurring, and that this may be demonstrated mathematically by showing the truth of P(A & B) = P(A) x P(B).
Mathematics (2019) Grade(s): 8 - Grade 8 Accelerated

MA19.8A.45

Compute the conditional probability of event A given event B, using two-way tables or tree diagrams. [Algebra I with Probability, 39]

Unpacked Content

UP:MA19.8A.45

Vocabulary

  • Conditional probability
  • Independence
  • Probability
  • Sample space
  • Simple event
  • Compound event

Knowledge

Students know:
  • Methods to find probability of simple and compound events.
  • Techniques to find conditional probability.

Skills

Students are able to:
  • Accurately determine the probability of simple and compound events.
  • Accurately determine the conditional probability P(A given B) from a sample space or from the knowledge of P(A&B) and the P(B).

Understanding

Students understand that:
  • The independence of two events is determined by the effect that one event has on the outcome of another event.
  • The occurrence of one event may or may not influence the likelihood that another event occurs.
Mathematics (2019) Grade(s): 8 - Grade 8 Accelerated

MA19.8A.46

Recognize and describe the concepts of conditional probability and independence in everyday situations and explain them using everyday language. [Algebra I with Probability, 40]

Unpacked Content

UP:MA19.8A.46

Vocabulary

  • Conditional probability
  • Independence
  • Probability

Knowledge

Students know:
  • Possible relationships and differences between the simple probability of an event and the probability of an event under a condition.

Skills

Students are able to:
  • Communicate the concepts of conditional probability and independence using everyday language by discussing the impact of the occurrence of one event on the likelihood of the other occurring.

Understanding

Students understand that:
  • The occurrence of one event may or may not influence the likelihood that another event occurs (e.g., successive flips of a coin
  • First toss exerts no influence on whether a head occurs on the second, drawing an ace from a deck changes the probability that the next card drawn is an ace).
  • Events are independent if the occurrence of one does not affect the probability of the other occurring.
Mathematics (2019) Grade(s): 8 - Grade 8 Accelerated

MA19.8A.47

Explain why the conditional probability of A given B is the fraction of B’s outcomes that also belong to A, and interpret the answer in context. [Algebra I with Probability, 41]

Unpacked Content

UP:MA19.8A.47

Vocabulary

  • Conditional probability
  • Probability
  • Simple events
  • Compound events
  • Sample space
  • Independent events
  • Dependent events

Knowledge

Students know:
  • Possible relationships and differences between the simple probability of an event and the probability of an event under a condition.

Skills

Students are able to:
  • Accurately determine the probability of simple and compound events.
  • Accurately determine the conditional probability P(A given B) from a sample space or from the knowledge of P(A&B) and the P(B).

Understanding

Students understand that:
  • Conditional probability is the probability of an event occurring given that another event has occurred.
Link to Resource
https://aptv.pbslearningmedia.org/resource/nvpn-sci-sarops/using-probability-in…

CR Resource Type

Audio/Video

Resource Provider

PBS
Accessibility

Accessibility

Video resources: includes closed captioning or subtitles
License

License Type

CUSTOM

Custom License Type (URL)

https://aptv.pbslearningmedia.org/help/terms-of-use/#.YD-bCNhKiUk

Approved Date

ALSDE LOGO

This site may contain links to other websites or content belonging to or originating from third parties or links to websites and features in banners or other advertising. Such external links are not investigated, monitored, or checked for accuracy, adequacy, validity, reliability, availability, or completeness by us. WE DO NOT WARRANT, ENDORSE, GUARANTEE, OR ASSUME RESPONSIBILITY FOR THE ACCURACY OR RELIABILITY OF ANY INFORMATION OFFERED BY THIRD-PARTY WEBSITES LINKED THROUGH THIS SITE.
Alabama Learning Exchange © 2002-2023 by Alabama State Department of Education is licensed under Attribution-NonCommercial-ShareAlike 4.0 International

Design by Adaptive Theme