Suppose we have four boxes A , B , C , D containing coloured marbles as given below: Marble Colour Box Red White Black A 1 6 3 B 6 2 2 C 8 1 1 D 0 6 4 One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A ? box B ? box C ?

Let R be the event that red marble is drawn. Let A be the event that the marble is drawn from box A , B be the event that the marble is drawn from box B , C be the event that the marble is drawn from box C and D be the event that the marble is drawn from box D Since, there are four boxes, so probability of choosing a box is same i.e. P ( A ) = P ( B ) = P ( C ) = P ( D ) = 1 4 Now, Probability that a red marble is chosen from box A i.e. P ( R A ) = 1 10 since there is one red and total ten marbles in the box A Similarly, probability that a red marble is chosen from box B i.e. P ( R B ) = 6 10 since there are 6 red and total ten marbles in box B . Similarly, probability that a red marble is chosen from box C i.e. P ( R C ) = 8 10 And probability that a red marble is chosen from box D i.e. P ( R D ) = 0 10 Now, we need to find the probability that the box A was chosen knowing that the marble drawn was red i.e. we need to find P ( A R ) So, by Bayes theorem, P ( A R ) = P ( A ) · P ( R A ) P ( A ) · P ( R A ) + P ( B ) · P ( R B ) + P ( C ) · P ( R C ) + P ( D ) · P ( R D ) = 1 4 · 1 10 1 4 · 1 10 + 1 4 · 6 10 + 1 4 · 8 10 + 1 4 · 0 10 = 1 40 15 40 = 1 15 Now, we need to find the probability that the box B was chosen knowing that the marble drawn was red i.e. we need to find P ( B R ) So, by Bayes theorem, P ( B R ) = P ( B ) · P ( R B ) P ( A ) · P ( R A ) + P ( B ) · P ( R B ) + P ( C ) · P ( R C ) + P ( D ) · P ( R D ) = 1 4 · 6 10 1 4 · 1 10 + 1 4 · 6 10 + 1 4 · 8 10 + 1 4 · 0 10 = 6 40 15 40 = 6 15 Now, we need to find the probability that the box C was chosen knowing that the marble drawn was red i.e. we need to find P ( C R ) So, by Bayes theorem, P ( C R ) = P ( C ) · P ( R C ) P ( A ) · P ( R A ) + P ( B ) · P ( R B ) + P ( C ) · P ( R C ) + P ( D ) · P ( R D ) = 1 4 · 8 10 1 4 · 1 10 + 1 4 · 6 10 + 1 4 · 8 10 + 1 4 · 0 10 = 8 40 15 40 = 8 15

A letter is known to have come either from LONDON or CLIFTON On the envelope just two consecutive letters ON are visible What is the probability that the letter has come from LONDON

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 12 - Probability>EXERCISE>Q 8

A letter is known to have come either from LONDON or CLIFTON. On the envelope just two consecutive letters ON are visible. What is the probability that the letter has come from CLIFTON?

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 12 - Probability>EXERCISE>Q 9

In a class,

5 %

of the boys and

10 %

of the girls have an $I Q$ of more than

150

. In this class,

60 %

of the students are boys. If a student is selected at random and found to have an $I Q$ of more than

150

, find the probability that the student is a boy.

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 12 - Probability>EXERCISE>Q 10

A factory has three machines $X, Y$ and $Z$ producing $1000, 2000$ and $3000$ bolts per day respectively. The machine $X$ produces $1 %$ defective bolts, $Y$ produces $1.5 %$ and $Z$ produces $2 %$ defective bolts. At the end of a day, a bolt is drawn at random and is found to be defective. What is the probability that this defective bolt has been produced by machine $X ?$

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 12 - Probability>EXERCISE>Q 11

An insurance company insured $3000$ scooters, $4000$ cars and $5000$ trucks. The probabilities of the accident involving a scooter, a car and a truck are $0.02, 0.03$ and $0.04$ respectively. One of the insured vehicles meet with an accident. Find the probability that it is a scooter.

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 12 - Probability>EXERCISE>Q 11

An insurance company insured $3000$ scooters, $4000$ cars and $5000$ trucks. The probabilities of the accident involving a scooter, a car and a truck are $0.02, 0.03$ and $0.04$ respectively. One of the insured vehicles meet with an accident. Find the probability that it is a car.

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 12 - Probability>EXERCISE>Q 11

An insurance company insured $3000$ scooters, $4000$ cars and $5000$ trucks. The probabilities of the accident involving a scooter, a car and a truck are $0.02, 0.03$ and $0.04$ respectively. One of the insured vehicles meet with an accident. Find the probability that it is a truck.

HARD

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 12 - Probability>EXERCISE>Q 12

Suppose we have four boxes $A, B, C, D$ containing coloured marbles as given below:

Marble Colour Box	Red	White	Black
$A$	$1$	$6$	$3$
$B$	$6$	$2$	$2$
$C$	$8$	$1$	$1$
$D$	$0$	$6$	$4$

One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box $A ?$ box $B ?$ box $C ?$

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 12 - Probability>EXERCISE>Q 13

A manufacturer has three machine operators $A, B$ and $C$ . The first operator $A$ produces $1 %$ defective items, whereas the other two operators $B$ and $C$ produce $5 %$ and $7 %$ defective items respectively. $A$ is on the job for $50 %$ of the time, $B$ on the job for $30 %$ of the time and $C$ on the job for $20 %$ of the time. A defective item is produced. What is the probability that it was produced by $A ?$

A letter is known to have come either from LONDON or CLIFTON. On the envelope just two consecutive letters ON are visible. What is the probability that the letter has come from LONDON

Important Questions on Probability

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