VIBRANT ACADEMY MATHS
Daily Practice Problems
(India) Private Limited Target IIT JEE
CLASS : MEGA-XII (ALL) SPECIAL DPP ON PROBABILITY DPP. NO.-1
1. 6 married couples are standing in a room. If 4 people are chosen at random, then the chance that exactly one
married couple is among the 4 is :
16 8 17 24
(A) (B) (C) (D)
33 33 33 33
2. A committee of 5 is to be chosen from a group of 9 people. The probability that a certain married couple will
either serve together or not at all is :
(A) 1/2 (B) 5/9 (C) 4/9 (D) 2/3
3. A quadratic equation is chosen from the set of all the quadratic equations which are unchanged by squaring
their roots. The chance that the chosen equation has equal roots is :
(A) 1/2 (B) 1/3 (C) 1/4 (D) 2/3
4. The probability that a positive two digit number selected at random has its tens digit at least three more than
its unit digit is
(A) 14/45 (B) 7/45 (C) 36/45 (D) 1/6
5. A 5 digit number is formed by using the digits 0, 1, 2, 3, 4 & 5 without repetition. The probability that the
number is divisible by 6 is :
(A) 8 % (B) 17 % (C) 18 % (D) 36 %
6. There are 'm' 10 rupees and 'n' 5 rupees coins placed at random in a line. Find the chance of the extreme
coins being both ten rupees.
7. A card is drawn at random from a well shuffled deck of cards. Find the probability that the card is a
(i) king or a red card (ii) club or a diamond (iii) king or a queen
(iv) king or an ace (v) spade or a club (vi) neither a heart nor a king.
8. A bag contain 5 white, 7 black, and 4 red balls, find the chance that three balls drawn at random are all
white.
9. If four coins are tossed, Two events A and B are defined as
A: No two consecutive heads occur
B: At least two consecutive heads occur.
Find P(A) and P(B). State whether the events are equally likely, mutually exclusive and exhaustive.
10. Thirteen persons take their places at a round table, Find the odds against two particular persons sitting
together.
SPECIAL DPP ON PROBABILITY_XII
11. A has 3 shares in a lottery containing 3 prizes and 9 blanks, B has 2 shares in a lottery containing 2 prizes
and 6 blanks. Compare their chances of success.
12. There are three works, one consisting of 3 volumes, one of 4 and the other of one volume. They are placed on
a shelf at random, find the chance that volumes of the same works are all together.
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13. 5 persons entered the lift cabin on the ground floor of an 8 floor building. Suppose that each of them
independently and with equal probability, can leave the cabin at any other floor, starting from the first, find the
probability that all 5 persons leave at different floors.
14. Consider a function f (x) that has zeroes 4 and 9. Given that Mr. A randomly selects a number from the set
{– 10, – 9, – 8, ..... 8, 9, 10}, what is the probability that Mr. A chooses a zero of f (x2)?
15. (a) A fair die is tossed. If the number is odd, find the probability that it is prime.
(b) Three fair coins are tossed. If both heads and tails appear, determine the probability that exactly one head
appears.
16. 3 boys and 3 girls sit in a row. Find the probability that (i) the 3 girls sit together. (ii) the boys are girls sit in
alternative seats.
17. A coin is biased so that heads is three times as likely to appear as tails. Find P (H) and P (T). If such a coin
is tossed twice find the probability that head occurs at least once.
18. Nine number 1, 2, 3, ......, 9 are put into a 3 × 3 array so that each number occur exactly once. Find the
probability that the sum of the numbers in atleast one horizontal row is greater than 21.
19. Mr. A lives at origin on the cartesian plane and has his office at (4, 5). His friend lives at (2, 3) on the same
plane. Mr. A can go to his office travelling one block at a time either in the + y or + x direction. If all possible
paths are equally likely then the probability that Mr. A passed his friends house is
(A) 1/2 (B) 10/21 (C) 1/4 (D) 11/21
20. In a game of cards, 52 playing cards are equally distributed among 4 players what is the chance that the
4 kings are held by a specified player?
ANSWER KEY
DPP-1
n ( n 1)
1. A 2. C 3. A 4. A 5. C 6.
( m n )( m n 1)
7. (i) 7/13, (ii) 1/2, (iii) 2/13, (iv) 2/13, (v) 1/2, (vi) 9/13 8. 1/56
9. 1/2 ; 1/2 10. 5:1 11. 952 to 715 12. 3/140
13. n(S) = 85; n(A) = 8C5 · 5! 14. 4/21 15. (a) 2/3, (b) 1/2 16. 1/5, 1/10
4
C4· 48C9
SPECIAL DPP ON PROBABILITY_XII
17. 3/4, 1/4, 15/16 18. 1/7 19. B 20. 52
C13
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