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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 :

ajeigbeibraheem

Answer:

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)

[tex]0.11 = \dfrac{13}{15}(0.09)+ \dfrac{2}{15}(x)[/tex]

[tex]0.11 - \dfrac{13}{15}(0.09)= \dfrac{2}{15}(x)[/tex]

[tex]0.032= 0.133(x)[/tex]

make x the subject of the formula:

x =  0.032/0.133

x = 0.24

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