The chance of a student passing an exam is 20%. The chance of a student passing the exam and getting above 90% marks in it is 5%. GIVEN that a student pass the examination, the probability that the student gets above 90% marks is:
Question
The chance of a student passing an exam is 20%. The chance of a student passing the exam and getting above 90% marks in it is 5%. GIVEN that a student pass the examination, the probability that the student gets above 90% marks is:
Solution
To solve this problem, we need to use the concept of conditional probability.
Step 1: Identify the given probabilities. The probability of a student passing the exam, P(Pass) = 20% or 0.20. The probability of a student passing the exam and getting above 90% marks, P(Pass and >90%) = 5% or 0.05.
Step 2: Apply the formula for conditional probability. The formula for conditional probability is P(A|B) = P(A and B) / P(B). In this case, we want to find the probability of a student getting above 90% marks GIVEN that they pass the exam. So, A is the event of getting above 90% marks and B is the event of passing the exam.
Step 3: Substitute the given values into the formula. P(>90%|Pass) = P(Pass and >90%) / P(Pass) = 0.05 / 0.20 = 0.25 or 25%.
So, given that a student passes the examination, the probability that the student gets above 90% marks is 25%.
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