GATE Overflow Test Series | Mock GATE | Test 1 | Question: 58

Question

A school has three divisions-- $A,B$ and $C$ for the tenth grade, having the number of students $40, 45$ and $42$ respectively. The pass percentages of students from the three divisions are $96, 97$ and $98$ respectively. If a student is chosen at random from the tenth grade and is found to have failed in the exam, what is the probability that it he/she is from the $A$ grade? (Rounded to $2$ decimal points)

Answer 1

Required Probability $=P(A|f) = \dfrac{P(A \cap f)}{P(f)} $

$\quad = \dfrac{\frac{40}{127} \times 0.04}{\frac{40}{127} \times 0.04 + \frac{45}{127} \times 0.03 + \frac{42}{127} \times 0.02} =0.4221.$

Comments

@gatecse

Number of failed students in A = 40 – 40*0.96 =(approximately) 2

Number of failed students in B = 45 – 45*0.97 = (approx) 2

Number of failed students in C = 42 – 42*0.98 = (approx) 1

 

P(A|f) = (number of failed students in A)/(number of failed students)

p(A|f) = (2/5)

= 0.4

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@gatecse Can you please clarify above comment? I have also solved the problem in the similar manner. Thanks.