1. Objective: To use probability calculations to determine the chance of success of a Search and Rescue mission Probability lesson SaRprobability.lgfl.net

2. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net Job Requirements Maths required: Calculate percentages Multiply decimals Calculate area Identify sequences Equipment required: Protractor Ruler Pencil Pen Rubber

3. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net Videos Introduction to the Coastguard What challenges does the Coastguard face? Why is Maths so important in Search and Rescue activities?Why is Maths so important in Search and Rescue activities?

4. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net Key terms POC – Probability of Containment - The probability of the search object being contained in the boundaries of some area. POD – Probability of Detection - The probability of detecting the search object. POS – Probability of Success - The probability that the search object will be found. POS = POC x POD

5. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net Example A ship has capsized in a fierce storm at night, and the search and rescue helicopter team has been called out to assist. Based on the poor conditions, and the helicopter’s endurance of 4 hours, the helicopter can only search an area of 2 square miles. Based on the conditions, the POC is 60% and the POD is only 40%. Calculate the POS (Probability of Success). POS = POC x POD = 0.6 x 0.4 = 0.24 = 24%

6. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net Example (part 2) The helicopter could choose to fly a little faster and cover a larger area. However, this will also reduce its ability to detect objects. By flying faster, it can cover an area of 8 square miles which gives a POC of 80%. But, it’s new POD is only 20% as it has less time to survey each part of the water. The new POS = POC x POD = 0.8 x 0.2 = 0.16 = 16% In this case, the initial search area had a better chance of finding the ship.

7. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net Determining search areas The Coastguard has to develop efficient search techniques. The speed a helicopter travels determines its ability to detect search objects. Distance travelled = 48 squares x 0.5 miles each = 24 miles 1 mile Area covered ≈ 4 x 4 = 16 miles 2 0.5 miles

8. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net POD tables The following table shows POD (Probability of detection) by a helicopter at various speeds in various conditions. This assumes a field of vision of 0.5 miles (as shown in previous example). 10mph20mph40mph Clear conditions100%80%60% Poor conditions80%60%30% Storm conditions60%40%10%

9. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net Determining POD In this example, in clear conditions we can find the time taken to search this area and the resulting POD. 10mph (100% POD): 24/10 = 2.4 hours 20mph (80% POD): 24/20 = 1.2 hours 40mph (60% POD): 24/40 = 0.6 hours Distance travelled = 48 squares x 0.5 miles each = 24 miles 1 mile Area covered ≈ 4 x 4 = 16 miles 2

10. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net Things to consider Why might the helicopter need to search a larger area? What are the benefits and drawbacks of searching a smaller area? How could you work out the time taken to cover a given search area?