While working for Life magazine Archie is assigned to the Ga

While working for Life magazine, Archie is assigned to the Galapagos Islands to photograph a rare, giant white turtle. The turtle can be found either on Isabella, the largest of the 16 Galapagos islands, or on Santa Cruz, the next largest island. Many have tried to locate the giant turtle, but 93% of them have failed. In addition, 13 out of every 15 searches in the past were concentrated on Santa Cruz, though only 5% of them were actually successful. Archie intends to search on Isabella. What is the probability that Archie will successfully find the turtle?

Round your answer to two decimal places.

Solution

Since 88% of all expeditions are failures, then it can be assumed that 12% are successes. That\'s the overall success rate of both islands. Since 9/12 of the searches are in the Santa Cruz area, then it can be assumed that the other 3/12 take place in Isabella. If Santa Cruz alone has a 9% success rate, then you need to have a success rate for Isabella that will balance out to equal the overall 12%. Since 9% is less than 12%, the success rate for Isabella will have to be larger. Keep that in mind. Your problem should look like this: (3x+9(.09))/12 = .12 Since 3 and 9 add up to 12, the denominator, then you have to find the success rate particular to Isabella, X, by dividing overall success rate by the particular success rate multiples by the overall attempts of Santa Cruz. Since the denominator is 12, you can multiple that times the overall success rate to get it out of the way. 3x+9(.09) = 1.44 x = 0.21 Success rate of Isabella is 21%