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Of the students in a school, it is known that 30% have 100% attendance and 70% students are irregular. Previous year results report that 70% of all students who have 100% attendance attain A grade and 10% irregular students attain A grade in their annual examination. At the end of the year, one student is chosen at random from the school and he was found to have an A grade. What is the probability that the student has 100% attendance ? Is regularity required only in school ? Justify your answer.

 

 

 

 
 
 
 
 

Answers (1)

consider E_{1}= the student has 100 %  attendance
               E_{2}= the student is irregular
             A: the student has grade A
Probability of the students having 100 % attendance
p\left ( E_{1} \right ) = 30\, ^{0}/_{0}= 0\cdot 3           p\left ( E_{2} \right ) = 70\, ^{0}/_{0}= 0\cdot 7
Now By previous year report    Probability of students having grade A who have 100 % attendance
p\left (\frac{A}{E_{1}}\right ) = 70\, ^{0}/_{0}= 0\cdot 7
p(students having grade A who are irregular)
p\left (\frac{A}{E_{2}}\right ) = 10\, ^{0}/_{0}= 0\cdot 1
Then the probablity of students having 100 % attendance who already has attain A grade = p\left ( \frac{E_{1}}{A} \right ) By Bayes' theorem
p\left ( \frac{E_{1}}{A} \right )= \frac{p\left ( \frac{A}{E_{1}} \right )p\left ( E_{1} \right )}{p\left ( \frac{A}{E_{1}} \right )p\left ( E_{1} \right )+p\left ( \frac{A}{E_{2}} \right )p\left ( E_{2} \right )}
  = \frac{0\cdot 7\times 0\cdot 3}{0\cdot 7\times 0\cdot 3+0\cdot 1\times 0\cdot 7}= \frac{21}{21+7}= \frac{21}{28}= \frac{3}{4}= 75\, ^{0}/_{0}
No, regularly is required in school as well as in life It helps to be diciplined in every aspect of life or when you work regularly, inspiration strikes regularly,

Posted by

Ravindra Pindel

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