3. Melissa needs to rent Limousines for her wedding. She has the choice between

Question

3. Melissa needs to rent Limousines for her wedding. She has the choice between sedan style Limousines and SUV styled limousines; W hite and Pink only. She found a Limo company with 19 SUV limousines (7 whites) and 24 Sedan Style Limous If Melis sa selects a Limousine and it is pink. What, then, is the probability that the limousine is a SUV? P (SUV/pink)? Construct a contingency table for the above scenario Please first display all the joints and marginal probabilities Show your answer to the conditional probability in all 3 methods learned in class (From the table, General conditional, Bayes' theorem) a. C.

Explanation / Answer

(a)

Following is the completed contingency table:

(b)

To find the joint and marginal probability distribution we need to divide each value by 43. Following table shows the joint and marginal probability distributions:

(c)

By table:

P(SUV|Pink) = 12 /21 = 0.5714

By general conditional probability:

P(SUV|Pink) =P(SUV and Pink) / P(pink) = 0.2791 / 0.4884 = 0.5715

By Baye's theorem:

P(pink | SUV) = 12/19

P(SUV) = 19/43

P(pink | Sedan) = 9/24

P(Sedan) = 24/43

P(SUV|Pink) = [ P(pink |SUV)P(SUV) ] / [P(pink |SUV)P(SUV)+P(pink |Sedan)P(Sedan)] = 0.5715

SUV Sedan Total Pink 12 9 21 White 7 15 22 Total 19 24 43

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