During the Cold War, Russian submarines would post as close as they could to the west coast of the US. In the case of an ordered attack on the US, or need to retaliate, basically to give them and edge or an upper hand they would be prepared to engage in offense. The US air force knew of their activities in the water, but didn't know exactly where they would be posted. S2 aircrafts were sent out either from a post on land or a carrier to search for the submarine. Through their search patterns when the enemy submarine has been located the S2 will hover over the submarine. An aircraft only has so much fuel before it needs to return to its post and refuel. At the time the pilot realizes he needs to refuel, they notifies the base where they came from for the base to send out another aircraft to be sent to the location the air craft, who is running out of fuel, last was (i.e. where the submarine was located). The first aircraft cannot wait until the second aircraft comes to take its location. So it leaves its position before the second aircraft arrives. Note, when US S2 aircrafts spotted the Russian submarines, the submarines know that they had been located. So when the first aircraft leaves before the second one arrives, the submarine has a certain amount of time to move from its previous location and cause the US to begin searching for it again. We are tasked with trying to find the probability of the second aircraft finding the submarine during the gap or lapse of time between aircraft 1 leaving its set position where the submarine is, and aircraft 2 returning to the position of aircraft one. State assumptions