Question

In an exam, there is a problem that 60% of students know the correct answer. However, thereis 15% chance that a student picked the wrong answer even if he/she knows the right answer andthere is also a 25% chance that a student does not know the right answer but guessed it correctly.If a student did get the problem right, what is the probability that this student really knows theanswer?

Answer 1

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) = $\frac{P(Student knew answer) X P(Student answered wrong given he knew the answer}{0.39}$

=$\frac{0.6*0.15}{0.39}$

=$\frac{0.09}{0.39}$

= 0.23076923077

= 0.231