# BHARDWAJ CLASSES

## CBSE CLASS 12 PROBABILITY IMPORTANT QUESTIONS WITH ANSWERS

### 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)
Also Read : Integration By Parts Practice Sheet

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

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