## CBSE CLASS 12 PROBABILITY IMPORTANT QUESTIONS WITH ANSWERS

Also Read : CBSE Class 12 Maths Sample Paper 2018

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PROBABILITY IMPORTANT PROBLEMS WITH ANSWERS

**1.**If A and B are two events such that P (A / B) = p, P(A) = p, P (B) = 1/3 and P ( A ⋃ B ) = 1/9, then p equal to?

**2.**In a school, there are 1000 students,out of which 430 are girls. It is known that out of 430, 10% of the girls study in class XII . What is the probability that a student chosen randomly studies in class XII, given that the chosen students is a girl?

**(**

**CBSE 2009)**

**3.**A die is thrown twice and the sum of the numbers appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once?

**(CBSE 2000)**

**4.**A family has two children. What Is the probability that both the children are boys, given that

**i)**at least one of them is a boy

**ii)**the elder child is a boy

**(**

**CBSE 2008,2010)**

**5.**12 cards numbered 1 to 12, are placed in a box, mixed up trolley and then one card is drawn at random from the box. if it is known that the number on the drawn card is more than 3 find the probability that it is an even number.

**(**

**CBSE 2008)**

**6.**A die is thrown, if E is the event ‘the number appearing is a multiple of 3’ and F be the event ‘the number appearing is even’, then find probability of E, probability of Fand check whether E and F are independent.

**(**

**Uttarakhand Board 2014 )**

**7.**A coin is tossed thrice and all 8 outcomes are equal likely A : “ the First result in head” , B: “ the last through result in tail” prove that the events a, b are independent .

**(**

**CBSE 2001)**

**8.**The probability of a solving a problem is 3 / 7 and that of B solving it is 1 / 3. what is the probability that

**i)**at least one of them will solve the problem,

**ii)**only one of them will solve the problem

**(**

**CBSE 2003)**

**9.**3 bag contains 7 white, 8 red; 9 whitet, 6 red and 5 white, 7 red balls respectively 1 ball drawn at random is drawn from each bag.Find the probability that all of the same colour.

**(CBSE 2000)**

**10.**A bag I contains 3 red and 4 white balls, another bag II contains 5 red and 6 white balls. one of the bag is selected at random and a ball is drawn from it, which is found to be red. find the probability that that the ball drawn is from bag 2 .

**(Uttarakhand Board**

**2014)**

**11.**A bag I contains 3 white and 2 red balls and a bag II contains 4 white and 5 red balls. one ball is drawn at random from one of the bags and is found to be red. find the probability that it was drawn from bag II.

**(**

**CBSE 2006, 2007)**

**12.**An insurance company insured 3000 scooters, 4000 cars and 5000 trucks.The probabilities of an accident involving a scooter comma a car anda truck or 0.02 , 0.03 and 0.04 respectively, one of the institute vehicle meets with an accident. find the probability that -

**i)**it is a scooter

**ii)**it is a car

**iii)**it is a truck

**(**

**CBSE 2011)**

**13.**2 urns contains 1 white, 6 red and 4 white, 3 red balls one of the urn is selected at random and a ball is drawn from it find:

**i)**the probability of drawing a white ball.

**ii)**the probability of drawing the ball from first and if ball drawn is white.

**(CBSE 2005)**

**14.**For A, B and C the chances of being selected as the manager of a firm are in the ratio 4: 1: 2 respectively, the respective probabilities of them to introduce a radical change in marketing strategy are 0.3, 0.8 and 0.5. if the change does take place find the probability that it is due to the appointment of B or C.

**(**

**CBSE 2005)**

**15.**A bag contains 4 balls, two balls are drawn at random and are found to be white. what is the probability that all balls are white.

**(**

**CBSE 2010 )**

**16.**Upkar manufacturing factory has two plants, X and Y. plant X manufacturers 70% of cars and plant Y manufacturers 30%. 80% of the cars at plant X and 90% of the cost at plant by are rated of standard quality. a car is selected at random and is found to be of standard quality. what is the probability that it has come from plant X.

**(CBSE 2000,2005)**

**17.**Given three identical boxes I,II and III, each containing two coins. In box I both coins are gold coins, in box II both are silver coins and in the third box III there is one gold and one silver coin. a person selected a box at random and takes out a coin. if the coin is of gold, what is the probability that the other coin in the box is also of gold?

**(**

**CBSE 2011)**

**18.**In a factory which manufactures bolts , Machine A, B and C manufacturer respectively 25%, 35% and 40% of the bolts. of their outputs 5 percent, 4 percent and 2 percent respectively defective bolts. A Bolt is drawn at random from the product and is found to be defective.

**i)**what is the probability that it is a manufactured by the machine B.

**ii)**find the probability that it is manufactured by either machine A or C.

**(CBSE 2003, 2010 , 2006, 2008, 2013)**

### ANSWERS OF PROBABILITY PROBLEMS

**1.**P = 1/3

**2.**0.1

**3.**2/5

**4.**i) 1/3 ii) 1/2

**5.**5/9

**6.**P(E) = 1/3

P(F) = 1/2 Eand Fare independent .

**8.**i) 14/15 ii) 2/5

**9.**217/900

**10.**35/68

**11.**25/43

**12.**i)3/19 ii) 6/19 iii) 10/19

**13.**i) 5/14 ii) 1/5

**14.**0.6

**15.**3/5

**16.**56/83

**17.**2/3

**18.**i) 28/69 ii) 41/69

**If You want Solution of these questions and any other help,Please let us know in Comment Section.**

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