Aptitude Questions on Probability

  1. In a cycle race there are 5 persons named as J,K,L,M,N participated for 5 positions. How many number of ways can M finishes always before N?
    A. 20
    B. 36
    C. 55
    D. 60
  2. D. 60
    Total number of ways in which 5 persons can finish is 5! = 120 (there are no ties)
    Now, in half of these ways M can finish before N
  3. A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
    A. 1/455
    B. 2/455
    C. 4/455
    D. 1/91
  4. A. 1/455
    Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
    Probability that all the three marbles picked at random are blue = 3C3 / 15C3 = (3 * 2 * 1) / (15 * 14 * 13) = 1/455
  5. The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
    A. 12/35
    B. 15/35
    C. 18/35
    D. 21/35
  6. C. 18/35
    If both agree stating the same fact, either both of them speak truth or both speak false.
    Probability = 3/5 * 4/7 + 2/5 * 3/7
    = 12/35 + 6/35 = 18/35
  7. If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is:
    A. 19/52
    B. 17/52
    C. 4/13
    D. 5/13
  8. C. 4/13
    P(SuK) = P(S) + P(K) - P(SnK), where S denotes spade and K denotes king.
    P(SuK) = 13/52 + 4/52 - 1/52 = 4/13
  9. Three 6 faced dice are thrown together. The probability that all the three show the same number on them is:
    A. 1/64
    B. 1/36
    C. 5/9
    D. 5/12
  10. B. 1/36
    If all 3 numbers have to be same; basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number.
    Further the three dice can fall in 6 * 6 * 6 = 216 ways
    Hence the probability is 6/216 = 1/36
  11. A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
    A. 17/91
    B. 33/91
    C. 51/91
    D. 65/91
  12. B. 33/91
    Given that there are 3 blue marbles, 4 red marbles, 6 green marbles and 2 yellow marbles.
    When 4 marbles are picked at random, then the probability that none is blue is = 12C4/15C4
    =>(12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91
  13. Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is:
    A. 13/21
    B. 10/19
    C. 11/15
    D. Cannot be determined
  14. D. Cannot be determined
    There is no definite formula for finding prime numbers among 15 consecutive numbers. Hence the probability cannot be determined.
  15. 10 books are placed at random in a shelf. The probability that a pair of books will always be together is:
    A. 1/10
    B. 1/5
    C. 3/10
    D. 9/10
  16. B. 1/5
    10 books can be rearranged in 10! ways
    Consider the 2 books taken as a pair then, number of favourable ways of getting these two books together is 9! 2!
    Required probability = 1/5
  17. The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is:
    A. 0.4869
    B. 0.5834
    C. 0.5904
    D. 0.6234
  18. C. 0.5904
    P(winning prize atleast on one ticket)
    = 1 - P('Losing on all tickets')
    = 1 - (0.8)^4 = (1 + (0.8)^2)(1 - (0.8)^2)
    = (1.64)(0.36) = 0.5904
  19. Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
    A. 1/2
    B. 2/5
    C. 8/15
    D. 9/20
  20. D. 9/20
    Here, S = {1, 2, 3, 4, ...., 19, 20}
    Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}
    P(E) = n(E)/n(S) = 9/20