## Bayes' Theorem: Solved Problems

Posted by vinod on Tuesday, April 14, 2015 Under: IIT,WBJEE,AIEEE

**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

and more problems like this

Download link: http://kolkatamaths.yolasite.com/resources/Bayes_Theorem.pdf

In : IIT,WBJEE,AIEEE