The Force is strong among the inhabitants of Tatooine the bi

The Force is strong among the inhabitants of Tatooine, the birthplace of Luke Skywalker. Not all of its inhabitants are capable of becoming a Jedi, but the probability is higher than among the rest of the members of the Alliance. Information was collected regarding this phenomena and it was determined that 54% of all of the members of the Alliance were born on Tatooine. It was also found that of all the members of the Alliance, 44% had the potential to become a Jedi. Finally, it was determined that 35% of all members of the Alliance were both from Tatooine and capable of becoming a Jedi. Based on this information calculate the following probabilities:

1. What is the probability that a member of the Alliance is randomly selected and found to be from Tatooine and not a Jedi?

2. What is the probability that a member of the Alliance is randomly selected and found to be from Tatooine or a Jedi?

3. What is the probability that a member of the Alliance is randomly selected and found to be neither from Tatooine nor a Jedi?

4. Given that a member of the Alliance is a Jedi, what is the probability that he/she is from Tatooine?

Solution

a Jedi

1.

P(from Tatooine and not a jedi) = P(from Tatooine) - P(from Tatooine and a Jedi) = 0.54-0.35 = 0.19

2.

P(from Tatooine or a jedi) = 0.35+0.19+0.09 = 0.63

3.

P(neither from Tatooine nor a jedi) = 1 - 0.63 = 0.37

4.

P(from Tatooine | a jedi) = 0.35/0.44 = 0.80