Class 12 ISC Maths Important Notes Chapter Probability

Probability Chapter Important Questions Class 12 ISC

Here we provide Class 12 Maths important questions,board questions and predicted questions with Answers for chapter Probability. These important notes,board questions and predicted questions are based on ISC board curriculum and correspond to the most recent Class 12 Maths syllabus. By practising these Class 12 materials, students will be able to quickly review all of the ideas covered in the chapter and prepare for the Class 12 Board examinations.

Select Option

Board Questions

Important Notes

Probability Important Questions

Q1 In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random find the probability that
(i) the student opted for NCC or NSS.
(ii) the student has opted neither NCC nor NSS.
(iii) the student has opted NSS but not NCC.

Solution

Q2 The probabilities that a student will get A, B, C or D grade are 0.4, 0.35 , 0.15 and 0.1 reapectively. Find the probability that she will get
(i) B or C grade (ii) atmost C grade.

Solution

Q3 A basket contains 20 apples and 10 oranges out of which 5 apples and 3 oranges are defective. If a person takes out 2 fruits at random , find the probability that either both are apples or both are good.

Solution

Q4 Two digits are selected at random from the digits 1 to 9. If the sum is even, then find probability that both digits are odd

Solution

Q5 (i) I roll two dice and get a sum more than 9. What is the probability that the number on the first die is even?
(ii) I roll two dice and get an even number on the first die. What is the probability that sum is more than 9?

Solution

Q6 60% students read Hindi newspaper, 40% students read Tamil newspaper and 20% students read both Hindi and Tamil newspaper. Find the probability that a student selected at random reads
(i) Tamil newspaper given that he has already read Hindi newspaper,
(ii) Hindi newspaper given that he has already read Tamil newspaper.
(iii) Neither Hindi nor Tamil newspaper.
what values are being promoted in this question

Solution

Q7 (i) If P(A) = 3/5 and P(B) = 1/5 then find P(A ∩ B) if A and B are independent events.
(ii) If A and B are two independent events such that P(not B) = 0.65 and P(A U B) = 0.85, then find P(A).

Solution

Q8 If P(A) = 0.2, P(B) = p, P(A U B) = 0.6 and A and B are given to be independent events, find the value of p.

Solution

Q9 One bag contains 3 white balls, 7 red balls and 15 black balls. Another bag contains 10 white balls, 6 red balls and 9 black balls. One ball is taken from each bag. Find the probability that both balls will be of the same colour.

Solution

Q10 Three cards are drawn from a pack of well-shuffled 52 cards. Find the probability that
(i) all the three cards are of the same suit
(ii) one is a king, the other is a queen and the third is a jack.

Solution

Q11 A bag contains 5 white and 4 black balls and another bag contains 7 white and 9 black balls. A ball is drawn from the first bag and two balls drawn from the second bag. What i5 the probability of drawing one white and two black balls?

Solution

Q12 (i) Kamal and Monika appear for an interview for two vacancies. The probability of Kamal's selection is 1/3 and that of Monika's selection is 1/5 . Find the probability that only one of them will be selected.
(ii) Akhil and Vijay appear for an interview for two vacancies. The probability of Akhil's selection is 1/4 and Vijay's selection is 2/3. Find the probability that only one of them 3 will be selected.

Solution

Q13 The probability of hitting a target at the first, second and third shots are
3 / 5
,
2 / 5
and
1 / 4
. Calculate the probability that the target gets hit.

Solution

Q14 A speaks truth in 75% of the cases, while B in 90% of the cases. In what percent of cads are they likely to contradict each other in stating the same fact?
Do you think that statement of B is true?

Solution

Q15 A bag contains 2 black, 4 white and 3 red balls. One ball is drawn at random and kept aside. Then another ball is drawn and kept aside. This process is continued till all the balls are drawn. Find the probability that the ball drawn are in the sequence 2 black. 4 white and 3 red.

Solution

Q16 Aman and Bhuvan throw a pair of dice alternately. In order to win, they have to get a sum of 8. Find their respective probabilities of winning if Aman starts the game.

Solution

Q17 There are three urns containing 2 white and 3 black balls, 3 white and 2 black balls, ate 4 white and 1 black ball, respectively. There is an equal opportunity of each urn ball chosen. A ball is drawn at random from the chosen urn and it is found to be white. Find the probability that ball drawn was from the second urn.

Solution

Q18 Urn I has 2 white and 3 black balls, urn II has 4 white and 1 black ball and urn III has 3 white and 4 black balls. An urn is selected at random and a ball is drawn at random.
(i) What is the probability of drawing a white ball?
(ii) If the ball drawn is white, then what is the probability that urn I was selected?

Solution

Q19 In a bolt factory, three machines A, B and C manufactures 25%, 35% and 40% of the total production respectively. Of their respective outputs, 5%, 4% and 2% are defective. A belt is drawn at random from the total production and it is found to be defective. Find the probability that it was manufactured by machine C.

Solution

Q20 A factory has three machines A, B and C producing 1500, 2500 and 3000 bulbs per day respectively. Machine A produces 15% defective bulbs, machine B products 2% defective bulbs and machine C produces 2.5% defective bulbs. At the end a bulb is drawn at random and it is found to be defective. What is the probability that this defective bulb has been produced by machine B?

Solution

Q21

An insurance company insured 4000 doctors, 8000 teachers and 12000 engineer, the probability of a doctor, a teacher and an engineer dying before the age of 58 are 0.01, 0.03 and 0.05 respectively. If one of the insured person dies before the age of 58 years, find the probability that he is a doctor.

Solution

Q22 The probability distribution of random variable X is given as under:

Where K is a constant calculate :
(i) the value of k
(ii) P(X ≥ 4)
(iii) E(X)

Solution

Q23 In a single throw of die random variable X defined as the number on its upper face, find the mean and variance of X.

Solution

Q24 Find the mean variance and standard deviation of the number of tales in 3 tosses of a coin.

Solution

Q25 And unbiased die is thrown twice, find the probability distribution of the number of sixes and hence find it's mean and variance.

Solution

Add a comment

Reach Us

SERVICES

ACADEMIC
ON-LINE PREPARATION
FOUNDATION & CRASH COURSES

CONTACT

B-54, Krishna Bhawan, Parag Narain Road, Near Butler Palace Colony Lucknow

Contact:+918081967119

Email:info@iqclasses.in

Probability Chapter Important Questions Class 12 ISC

Select Option

Solution

Q2 The probabilities that a student will get A, B, C or D grade are 0.4, 0.35 , 0.15 and 0.1 reapectively. Find the probability that she will get (i) B or C grade (ii) atmost C grade.

Solution

Q3 A basket contains 20 apples and 10 oranges out of which 5 apples and 3 oranges are defective. If a person takes out 2 fruits at random , find the probability that either both are apples or both are good.

Solution

Q4 Two digits are selected at random from the digits 1 to 9. If the sum is even, then find probability that both digits are odd

Solution

Q5 (i) I roll two dice and get a sum more than 9. What is the probability that the number on the first die is even? (ii) I roll two dice and get an even number on the first die. What is the probability that sum is more than 9?

Solution

Solution

Q7 (i) If P(A) = 3/5 and P(B) = 1/5 then find P(A ∩ B) if A and B are independent events. (ii) If A and B are two independent events such that P(not B) = 0.65 and P(A U B) = 0.85, then find P(A).

Solution

Q8 If P(A) = 0.2, P(B) = p, P(A U B) = 0.6 and A and B are given to be independent events, find the value of p.

Solution

Q9 One bag contains 3 white balls, 7 red balls and 15 black balls. Another bag contains 10 white balls, 6 red balls and 9 black balls. One ball is taken from each bag. Find the probability that both balls will be of the same colour.

Solution

Q10 Three cards are drawn from a pack of well-shuffled 52 cards. Find the probability that (i) all the three cards are of the same suit (ii) one is a king, the other is a queen and the third is a jack.

Solution

Q11 A bag contains 5 white and 4 black balls and another bag contains 7 white and 9 black balls. A ball is drawn from the first bag and two balls drawn from the second bag. What i5 the probability of drawing one white and two black balls?

Solution

Solution

Q13 The probability of hitting a target at the first, second and third shots are 3 / 5 , 2 / 5 and 1 / 4 . Calculate the probability that the target gets hit.

Solution

Q14 A speaks truth in 75% of the cases, while B in 90% of the cases. In what percent of cads are they likely to contradict each other in stating the same fact? Do you think that statement of B is true?

Solution

Q15 A bag contains 2 black, 4 white and 3 red balls. One ball is drawn at random and kept aside. Then another ball is drawn and kept aside. This process is continued till all the balls are drawn. Find the probability that the ball drawn are in the sequence 2 black. 4 white and 3 red.

Solution

Q16 Aman and Bhuvan throw a pair of dice alternately. In order to win, they have to get a sum of 8. Find their respective probabilities of winning if Aman starts the game.

Solution

Solution

Solution

Solution

Solution

Q21

Solution

Q22 The probability distribution of random variable X is given as under: Where K is a constant calculate : (i) the value of k (ii) P(X ≥ 4) (iii) E(X)

Solution

Q23 In a single throw of die random variable X defined as the number on its upper face, find the mean and variance of X.

Solution

Q24 Find the mean variance and standard deviation of the number of tales in 3 tosses of a coin.

Solution

Q25 And unbiased die is thrown twice, find the probability distribution of the number of sixes and hence find it's mean and variance.

Solution

Add a comment

Reach Us

SERVICES

CONTACT

Q2 The probabilities that a student will get A, B, C or D grade are 0.4, 0.35 , 0.15 and 0.1 reapectively. Find the probability that she will get
(i) B or C grade (ii) atmost C grade.

Q5 (i) I roll two dice and get a sum more than 9. What is the probability that the number on the first die is even?
(ii) I roll two dice and get an even number on the first die. What is the probability that sum is more than 9?

Q7 (i) If P(A) = 3/5 and P(B) = 1/5 then find P(A ∩ B) if A and B are independent events.
(ii) If A and B are two independent events such that P(not B) = 0.65 and P(A U B) = 0.85, then find P(A).

Q10 Three cards are drawn from a pack of well-shuffled 52 cards. Find the probability that
(i) all the three cards are of the same suit
(ii) one is a king, the other is a queen and the third is a jack.

Q13 The probability of hitting a target at the first, second and third shots are
3 / 5
,
2 / 5
and
1 / 4
. Calculate the probability that the target gets hit.

Q14 A speaks truth in 75% of the cases, while B in 90% of the cases. In what percent of cads are they likely to contradict each other in stating the same fact?
Do you think that statement of B is true?

Q22 The probability distribution of random variable X is given as under:

Where K is a constant calculate :
(i) the value of k
(ii) P(X ≥ 4)
(iii) E(X)