Mexican voters know that regardless of the candidates’ campaign promises, their
ID: 3282653 • Letter: M
Question
Mexican voters know that regardless of the candidates’ campaign promises, their actual performance in office will depend on whether they are a low (L) or a high (H) type. Suppose that a politician is a low type with probability ? = 1 2 , and the probability that she is a high type is 1 ? ?. Under both types of policitian you can see either a good economy (GE) or a bad economy (BE). The economy is more likely to be good when a high type is elected, so we make the following assumptions. The probability of having a good economy under a high type is ? = 0.6, and the probability of having a good economy under a low type is 1 ? ? = 0.4. Answer the following questions assuming the president has been in office for one term,
(a) What is the probability of having a good economy? [0.5 pt]
(b) What is the probability of having a good type of politician given that we have a good economy? [0.5 pt]
(c) What is the probability of having a bad type of politician given that we have a good economy? [0.5 pt]
Suppose the politician has been in office for three consecutive terms,
(a) What is the probability of having a good economy in the first two terms and a bad economy in the third term? [0.5 pt]
(b) What is the probability of having a good type given the state of the economy? [0.5 pt]
(c) What is the probability of having a bad type given the state of the economy? [0.5 pt]
Explanation / Answer
Solved the first scenario with three sub-parts for the next three sub-parts, post one more question as per Chegg guidelines
(There are question marks coming in the problem, if any of the data below is incorrect, modify the values in the expression below to get the final answer)
Probability that politician is a low type = 0.5
Probability that politician is a high type = 0.5
Probability that high type will have good economy = 0.6
Probability that low type will have good economy = 0.4
a) Probability of having a good economy = Probability that politician is a low type * Probability that low type will have good economy + Probability that high type will have good economy * Probability that politician is a high type
=> 0.5 * 0.4 + 0.6 * 0.5
=> 0.50
b) P(good type of politician|good economy) = (Probability that high type will have good economy * Probability that politician is a high type)/(Answer in Problem (a))
=> 0.30/0.50
=> 0.6
c) P(lowtype of politician|good economy) = (Probability that low type will have good economy * Probability that politician is a lowtype)/(Answer in Problem (a))
=> 0.20/0.50
=> 0.4