The chance of a student passing an exam is 30% , the chance of a student passing the exam and getting above 80% marks in it is 10%, if it is given that a student has passed the examination, then find the probability that the student has secure more than 80% marks in the exam ?
1. 3/8
2. 1/3
3. 1/9
4. 1/8
1. 3/8
2. 1/3
3. 1/9
4. 1/8
Correct Answer – Option 2 : 1/3
Concept:
P(A \(\cap\) B) = P(A) x P(B | A) = P(B) x P(A | B) where P(A | B) represents the conditional probability of A given B and P (A | B) represents the conditional probability of B given A.
Calculation:
Given: P(A student passing the exam) = 30% = 0.3, P(A student passing the exam and getting above 80% marks) = 10% = 0.1
The desired probability,
P(Student gets more than 80% marks | Student has passed the exam) = P(student passing the exam and gets more than 80% of marks) / P(Student has passed the exam)
⇒ P(Student gets more than 80% marks | Student has passed the exam) = 0.1/0.3
⇒ P(Student gets more than 80% marks | Student has passed the exam) = 1/3
Hence, option 2 is correct.