Let S be the sample space and A a subset of S
P(A)=n(A)/n(S)
P(S)=1
P( {} ) = 0, {} stands for null set
let A' denote the event that "A does not happen"
P(A) +P(A') =1
P(A') = 1-P(A)
P(A) = 1-P(A')
addition theorem
P[A ∪ B] = P(A) +P(B) - P[A∩B]
P[A or B] = P(A) +P(B) - P[A and B]
Bayes theorem
Total probability
problem 2
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.
solution to problem 2 of bayes theorem
problem 3
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
hostelier?
solution to problem 3 of bayes theorem
problem 4
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 ( 1/4) be the probability that he guesses. Assuming
that a student who guesses at the answer will be correct with
probability ( 1/4 ). What is the probability that the student knows the
answer given that he answered it correctly?
solution to bayes theorem problem 4 for ncert cbse 12th mathematics
problem 5
A laboratory blood test is 99% effective in detecting a certain disease
when it is in fact, present. However, the test also yields a false
positive result for 0.5% of the healthy person tested (i.e. if a healthy
person is tested, then, with probability 0.005, the test will imply he
has the disease). If 0.1 percent of the population actually has the
disease, what is the probability that a person has the disease given
that his test result is positive ?
solution to bayes theorem problem 5 for ncert cbse 12th mathematics
problem 6
There are three coins. One is a two headed coin (having head on both
faces),another is a biased coin that comes up heads 75% of the time and
third is an unbiased coin. One of the three coins is chosen at random
and tossed, it shows heads, what is the probability that it was the two
headed coin ?
solution to problem 6 of bayes theorem for cbse ncert mathematics
problem 7
An insurance company insured 2000 scooter drivers, 4000 car drivers and
6000 truck drivers. The probability of an accidents are 0.01, 0.03 and
0.15 respectively. One of the insured persons meets with an accident.
What is the probability that he is a scooter driver?
solution to problem 7 of bayes theorem for cbse ncert mathematics
problem 8
A factory has two machines A and B. Past record shows that machine A
produced 60% of the items of output and machine B produced 40% of the
items. Further,2% of the items produced by machine A and 1% produced by
machine B were defective. All the items are put into one stockpile and
then one item is chosen at random from this and is found to be
defective. What is the probability that it was produced by machine B?
solution of problem 8 on bayes theorem for cbse mathematics
problem 9
Two groups are competing for the position on the Board of directors of a
corporation. The probabilities that the first and the second groups
will win are 0.6 and 0.4 respectively. Further, if the first group wins,
the probability of introducing a new product is 0.7 and the
corresponding probability is 0.3 if the second group wins. Find the
probability that the new product introduced was by the second group.
solution of problem 9 on bayes theorem for cbse mathematics
problem 10
Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin
three times and notes the number of heads. If she gets 1, 2, 3 or 4, she
tosses a coin once and notes whether a head or tail is obtained. If she
obtained exactly one head, what is the probability that she threw 1, 2,
3 or 4 with the die?
solution of problem10 on bayes theorem for ncert cbse mathematics
problem 11
A manufacturer has three machine operators A, B and C. The first
operator A produces 1% defective items, where as the other two operators
B and C produce 5% and 7% defective items respectively. A is on the job
for 50% of the time, B is on the job for 30% of the time and C is on
the job for 20% of the time. A defective item is produced, what is the
probability that it was produced by A?
solution of problem11 on bayes theorem for ncert cbse mathematics
problem 12
A card from a pack of 52 cards is lost. From the remaining cards of the
pack,two cards are drawn and are found to be both diamonds. Find the
probability of the lost card being a diamond.
solution to bayes theorem problem 12 for ncert cbse mathematics probability
problem 13
Probability that a man speaks truth is ( 4 / 5 ). A coin is tossed and
the man reports that a head appeared.Find the probability that actually
there was a head.
solution to bayes theorem problem 13for ncert cbse mathematics probability
miscellaneous exercise problem 14
Assume that the chances 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 a 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?
solution to miscellaneous exercise problem 14 on bayes theorem in ncert cbse 12th mathematics
miscellaneous exercise problem 15
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.
solution to miscellaneous exercise problem 15on bayes theorem in ncert cbse 12th mathematics
disclaimer:
There is no guarantee about the data/information on this site. You use
the data/information at your own risk. You use the advertisements
displayed on this page at your own risk.We are not responsible for the
content of external internet sites. Some of the links may not work
bayes theorem is a topic for cbse / ncert / scert of 12th standard in
India. These are some of the important questions from the topic of bayes
theorem from various cbse ncert textbooks and old question paper
No comments:
Post a Comment
please leave your comments