Answer:
0.231
Step-by-step explanation:
Let the Probability of students that knew the correct answer be: P(A)
P(A) = 60% = 0.6
Let the Probability that the student picked the wrong answer even if he/she knows the right answer be: P(B)
P(B) = 15% =0.15
Let the Probability of the student that do not knew the correct answer Be P(C)
P(C) = 1 - P(A)
P(C) = 1 - 0.6
P(C) = 0.4
Let the Probability that the student does not know the right answer but guessed it correctly be: P(D)
P(D) = 25% = 0.25
Let the Probability that the student picked the right answer even if he/she knows the right answer be: P(E)
P(E) = 1 - P(B)
P(E) = 1 - 0.15
P(E) = 0.85
Probability that the student got the answer wrong = (0.60 X 0.15) + (0.40 X 0.75) = 0.39
P( Student knew answer given he answered wrong) = [tex]\frac{P(Student knew answer) X P(Student answered wrong given he knew the answer}{0.39}[/tex]
=[tex]\frac{0.6*0.15}{0.39}[/tex]
=[tex]\frac{0.09}{0.39}[/tex]
= 0.23076923077
= 0.231
