Master Yoda is collecting data about the Force. He mails a survey to households

ID: 2927651 • Letter: M

Question

Master Yoda is collecting data about the Force. He mails a survey to

households on Tatooine to determine the probability that a randomly selected person is

a Sith or a Jedi. Because Master Yoda is wise, he uses a decision tree to help provide

him the answers he seeks. His random sample results in the following information:

45% of the respondents are male, 55% are female and the remainder are

droids.

Of the males, 75% are Jedi and the remainder are Sith

Of the females, 25% are Sith and the remainder are Jedi

Of the droids, 25% are Siths and 75% are Jedi

If he randomly selects a survey from the responses received, what is the probability that:

a. The survey selected indicates a male Jedi?

b. The survey selected indicates Jedi but not a male?

c. The survey selected indicates a Sith?

d. The survey selected indicates a Jedi droid ?

e. The survey selected indicates female, but not Sith?

Answer to the question is as follows with calculations:

a. P( male jedi) = P(male)*P(given male, He' Jedi) = .45*75/1 = .3375

b. P(Jedi and not male) = P(Is not male )*P(non male is Jedi) = .55(.75)/1 = .4125

c. P( is a Sith) = .P(male)*P(given male , is a Sith) + P(given female, is a Sith) = 45*.25 +.55.75 / 1 = .525

d. P( is Jedi droid) = 0, as Droid consitute 1-.45-.55 = 0%age of the Force

e. P( female but not Sith) = P(is a female)(P(give female is a Sith) = .55*.75/1 = .5575