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Of the students in a college, it is know...

Of the students in a college, it is known that 60% reside in hostel and 40% are day scholars (not residing in hostel). Previous year results report that 30% of all students who reside in hostel attain A grade and 20% of day scholars attain A grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an A grade, what is the probability that the student is a hostlier?

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To solve the problem, we will use Bayes' theorem to find the probability that a student is a hosteler given that they have attained an A grade. ### Step-by-Step Solution: 1. **Define Events**: - Let \( E_1 \) be the event that a student is a hosteler. - Let \( E_2 \) be the event that a student is a day scholar (not a hosteler). - Let \( A \) be the event that a student attains an A grade. ...
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