A study of current SBU students showed that among \"working students,\" 80 now s
ID: 2946769 • Letter: A
Question
A study of current SBU students showed that among "working students," 80 now say that the "ideal situation is working while going to school." About 37% of the students in the survey did not work. Among "mon-working students," 48 percent say that the "ideal situation is not working while in school." percent Of the SBU students who believe that the "ideal situation is not working while in school," what percentage are "working students"? (6 points) 1. 2. What is the probability that a randomly selected SBU student will be a non working student" who also believes that hisher (non-working) situation is ideal? (6 points)Explanation / Answer
1) Here, we are given that:
P( say that working is ideal ) = 0.8
Therefore, P( say that not working is ideal ) = 1 - 0.8 = 0.2
P( did not work ) = 0.37, Therefore P( working ) = 1 - 0.37 = 0.63
P( say that not working is ideal | not working ) = 0.48
Therefore, P( say that working is ideal | not working ) = 1 - 0.48 = 0.52
Using law of total probability, we get here:
P( say that not working is ideal ) = P( say that not working is ideal | working ) P( working ) + P( say that not working is ideal | not working ) P( not working )
Putting all the given values, we get:
0.2 = P( say that not working is ideal | working ) *0.63 + 0.48*0.37
Therefore, P( say that not working is ideal | working ) = [ 0.2 - 0.48*0.37 ] / 0.63 = 0.0356
Using bayes theorem, we get:
P( working | say that not working is ideal ) = P( say that not working is ideal | working )P( working ) / P( say that not working is ideal )
P( working | say that not working is ideal ) = 0.0356*0.63 / 0.2 = 0.112
Therefore 11.2% is the required answer here.
2) P( non working student and say that not working is ideal) is computed using bayes theorem as:
P( non working student and say that not working is ideal) = P( say that not working is ideal | not working ) P( not working )
P( non working student and say that not working is ideal) = 0.48*0.37 = 0.1776
Therefore 0.1776 is the required probability here.
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