Consider in the 1st class of civil engineering department, 15% of stud

Douglas Kraatz

Douglas Kraatz

Answered question

2021-11-16

Consider in the 1st class of civil engineering department, 15% of students fail in mechanics, 10% of students fail in mathematics, and 7% of students fail in both. If a random student is selected, find:
1) Probability if he is good in mechanics to be bad in mathematics.
2) Probability if he is bad in mathematics to be bad in mechanics.
3) Probability if he is good in mathematics to be bad in mechanics.

Answer & Explanation

Unpled

Unpled

Beginner2021-11-17Added 23 answers

Step 1
Given:
P(fail in mechanics) =0.15
P(fail in mathematics) =0.10
p(fail in both) =0.07
Step 2
1. To find: P( bad in mathematics | good in mechanics)
Using the concept of Conditional probability , P(XY)=PX,YP(Y)
So, P( bad in maths | good in mechanics) = P( bad in maths and good in mechanics ) / P(good in mechanics)
P( good in mechanics) =1P ( fail in mechanics) =10.15=0.85
P( bad in maths and good in mechanics ) =0.100.85
Required probability =0.100.850.85=0.10
Step 3
2. To find: P( bad in mechanics | bad in mathematics)
Using the concept of Conditional probability , P(XY)=PX,YP(Y)
So, P( bad in mechanics | bad in maths) = P( bad in maths and bad in mechanics ) / P(bad in maths)
P(bad in maths ) =0.10
P( bad in maths and bad in mechanics ) =0.07
Required probability =0.070.10=0.7
Step 4
3. To find: P( bad in mechanics | good in maths)
Using the concept of Conditional probability , P(XY)=PX,YP(Y)
So, P( bad in mechanics | good in maths) = P( bad in mechanics and good in maths ) / P(good in maths)
P( good in maths) =0.90
P( good in maths and bad in mechanics ) =0.900.15
Required probability =0.900.150.90=0.15

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