Question

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 89% of them have failed. In addition, 13 out of every 15 searches in the past were concentrated on Santa Cruz, though only 9% of them were actually successful. Archie intends to search on Isabella. What is the probability that Archie will successfully find the turtle

Answer 1

The probability of Archie finding the turtle on Isabella can't be calculated directly, but based on the given information, it is likely to be higher than 9%.

Step-by-step explanation:

To calculate the probability that Archie will successfully find the turtle, we need to consider the information given. We know that 89% of search attempts in the past have failed, and that only 9% of searches on Santa Cruz were successful. However, the information doesn't provide the success rate for searches on Isabella.

Since we don't have the specific success rate for Isabella, we can't calculate the probability directly. However, we can make an assumption based on the given information. Since 13 out of every 15 searches in the past were concentrated on Santa Cruz and only 9% of them were successful, it suggests that the success rate on Isabella might be higher.

Therefore, based on this assumption, we could estimate Archie's probability of successfully finding the turtle on Isabella to be higher than 9%.

Answer 2

0.24

Step-by-step explanation:

From the information given:

Let's have a schematic view of a tree diagram

A

P(Santa Cruz) P(Isabella)

= 13/15 = 2/15

P(Success | Santa Cruz) = 0.09 P(Success | Isabella) = x

We are told that many have tried to locate the giant turtle, but 89% of them have failed.

This means the probability of success is:

P(success) = 1 - 0.89 = 0.11

We need to find P(Success | Isabella),

Suppose P(Success | Isabella) be x as shown above,

Then:

P (Success) = P(Santa) P((Success | Santa Cruz) + P(Isabella) P(Success | Isabella)

`0.11 = (13)/(15)(0.09)+ (2)/(15)(x)`

`0.11 - (13)/(15)(0.09)= (2)/(15)(x)`

`0.032= 0.133(x)`

make x the subject of the formula:

x = 0.032/0.133

x = 0.24