Solved Problems on Bayes' Theorem. NCERT Solutions

Question 1.


A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.

Question 2.
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?

Question 3.
In answering a question on a multiple choice test, a student either knows the
answer or guesses. Let 3/4 be the probability that he knows the answer and
¼ be the probability that he guesses. Assuming that a student who guesses at the
answer will be correct with probability ¼.What is the probability that the student knows the answer given that he answered it correctly?

Question 4.
Assume that the chance of a patient having a heart attack is 40%. It is also
assumed that a meditation and yoga course reduce the risk of heart attack by
30% and prescription of certain drug reduces its chances by 25%. At a time a
patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?

Question 5.
Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls.One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black.

Question 6.
Probability that A speaks truth is 4/5. A coin is tossed. A reports that a head
appears. Find the probability that actually there was head.

Question 7.
Vinod is known to speak truth 3 out of 4 times. He throws a die and
reports that it is a six. Find the probability that it is actually a six.

and more problems like this 
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