I can\'t seem to figure out this question. I think it has moreto do with the wor
ID: 2955078 • Letter: I
Question
I can't seem to figure out this question. I think it has moreto do with the wording of the question though. Below is thequestion:"The entering class in an engineering college has 34% who intend tomajor in mechanical engineering, 33% who indicate an interest intaking advanced courses in mathematics as part of their major fieldof study, and 28% who intend to major in electrical engineering,while 23% have other interests. In addition, 59% are known tomajor in mechanical engineering or take advanced mathematics, while51% intend to major in electrical engineering or take advancedmathematics. Assuming that a student can major in only onefield, what percent of the class intends to major in mechanicalengineering or in electrical engineering, but shows no interest inadvanced mathematics?"
The question seems confusing to me, because I took the 59% ofMechanical/Advanced Maths and subtracted the given 34% ofmechanicals, which gave me 25% of advanced math. Doing thesame thing for electricals yielded 23% advanced math. So I'mconfused why the two aren't the same, or maybe I'm looking at thiswrong...
Explanation / Answer
Step 1: Enter the marginal probabilities.
ME
EE
Oth Int
Missing
Math
0.33
Non-Math
0.37
0.34
0.28
0.23
0.15
1.00
Step 2: Find the joint probabilities using inclusion/exclusion formula.
P(A or B) = P(A) + P(B) –P(AB)
P(AB) = P(A) + P(B) – P(A or B)
P(ME & Math) = P(ME) + P(Math) – P(ME or Math)
= 0.34 + 0.33 – 0.59 = 0.05
P(EE & Math) = P(EE) + P(Math) – P(EE or Math)
= 0.28 + 0.33 – 0.51 = 0.10
ME
EE
Oth Int
Missing
Math
0.05
0.10
0.33
Non-Math
0.37
0.31
0.28
0.23
0.18
1.00
Step 3: Find the joint probabilities bysubtraction.
P(ME & Non-Math) = P(ME) – P(ME &Math) = 0.31 – 0.05 = 0.26
P(ME & Non-Math) = P(EE) – P(EE & Math) = 0.28– 0.10 = 0.18
P(ME or EE & Non-Math) = 0.26 +0.18 = 0.44
ME
EE
Oth Int
Missing
Math
0.05
0.10
0.33
Non-Math
0.26
0.18
0.37
0.31
0.28
0.23
0.18
1.00
ME
EE
Oth Int
Missing
Math
0.33
Non-Math
0.37
0.34
0.28
0.23
0.15
1.00
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