Question

Let's suppose that student A applied to two law schools (“X” and “Y “) in 2014. (So the program starts in 2015) If she graduates from the law school “X”, she gets payed $10000 /month but there is a 50 % chance that she loses her job within a year. If she graduates from the law school “Y”, she get payed $ 8000 / month but there is a 20 % chance that she loses her job within a year. She strictly prefers law school “X” to law school “Y”, so if she gets admitted into both schools, she will accept the law school “X”. ( Also, if she gets admitted to only one school, she will take that offer. If she does not get admitted into any of the programs, she pursues another career). The probability of being admitted into Law school X is 0.5, and the probability of being admitted to Law school Y is 0.5. And the probability of getting admitted into both schools is 0.25. Now, as of 2019, you know that the student A graduated from a law school in 2018 but lost her job one year after the graduation. What is the probability that she graduated from Law school “X”? (Calculate the result rounded to the second digit after the decimal point)

Answer 1