Probability

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Aptitude miscellaneous
  1. A card is drawn at random from a pack of 52 cards. A card is drawn at random. What is the probability that it is neither a heart nor a king ?








  1. View Hint View Answer Discuss in Forum

    There are 13 hearts and 3 more kings
    ∴ P(heart or a king) = (13 + 3)/52 = 4/13

    Correct Option: B

    There are 13 hearts and 3 more kings
    ∴ P(heart or a king) = (13 + 3)/52 = 4/13
    ∴ P (neither a heart nor a king) = 1 - 4/13 = 9/13

  1. Three mangoes and three apples are kept in a box. if two fruits are chosen at random. find the probability that one is a mango and the other is an apple.










  1. View Hint View Answer Discuss in Forum

    Total number of ways
    = n(s) = 6c2 = 15
    Favorable number of ways
    = n(E) = 3C1 x 3C1= 9

    Correct Option: B

    Total number of ways
    = n(s) = 6c2 = 15
    Favorable number of ways
    = n(E) = 3C1 x 3C1= 9
    ∴ Required probability = 9/15 = 3/5

  1. A box contains 3 white and 2 red balls. If we draw one ball and ball and without replacing the first ball. The probability of drawing red ball in the second drawn is ?








  1. View Hint View Answer Discuss in Forum

    Total balls in the box = 5
    Second red ball can be drawn in two ways
    Case I. First ball is white and second ball is red.
    Its probability = 3/5.2/4 = 6/20 = 3/10
    Case II: First ball is red and second ball is red
    Its probability = 2/5.1/4 = 2/20 = 1/10

    Correct Option: B

    Total balls in the box = 5
    Second red ball can be drawn in two ways
    Case I. First ball is white and second ball is red.
    Its probability = 3/5.2/4 = 6/20 = 3/10
    Case II: First ball is red and second ball is red
    Its probability = 2/5.1/4 = 2/20 = 1/10
    Hence, reqd. probability
    = 3/10 + 1/10 = 4/10 = 2/5

  1. if from each of the three boxes containing 3 white and 1 black, 2 white and 2 black and 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black ball will be drawn is ?








  1. View Hint View Answer Discuss in Forum

    You can have
    W, W, B or W, B, W or B, W, W

    Correct Option: A

    You can have
    W, W, B or W, B, W or B, W, W

    Reqd. probability
    = 3/4. 2/4. 3/4 + 3/4. 2/4. 1/4 + 1/4. 2/4. 1/4
    = 9/32 + 3/32 + 1/32 = 13/32

  1. The probability that a man will be alive for 10 more years is 1/4 and the probability that his wife will alive for 10 more years is 1/3 .The probability that none of them will be alive for 10 more years, is










  1. View Hint View Answer Discuss in Forum

    Required probability = P(A) x P(B)
    = (1 - 1/4) x (1 - 1/3)

    Correct Option: B

    Required probability = P(A) x P(B)
    = (1 - 1/4) x (1 - 1/3) = 3/4 x 2/3 = 1/2