Engineering Mathematics Miscellaneous


Engineering Mathematics Miscellaneous

Engineering Mathematics

  1. A coin is tossed 4 times. What is the probability of getting heads exactly 3 times?









  1. View Hint View Answer Discuss in Forum

    Number of favourable cases are given by
    H H H T
    H H T H
    H T H H
    T H H H
    Total number of cases = 2C1 × 2C1 × 2C1 × 2C1 = 16

    ∴ Probablity =
    4
    =
    1
    164

    Correct Option: A

    Number of favourable cases are given by
    H H H T
    H H T H
    H T H H
    T H H H
    Total number of cases = 2C1 × 2C1 × 2C1 × 2C1 = 16

    ∴ Probablity =
    4
    =
    1
    164


  1. A box contains 20 defective items and 80 nondefective items. If two items are selected at random without replacement, what will be the probability that both items are defective?









  1. View Hint View Answer Discuss in Forum

    P(Both defective) =
    N(Both defective)
    Sample space

    =
    20C2
    =
    19
    100C2495

    Correct Option: D

    P(Both defective) =
    N(Both defective)
    Sample space

    =
    20C2
    =
    19
    100C2495



  1. A single die is thrown twice. What is the probability that the sum is neither 8 nor 9?









  1. View Hint View Answer Discuss in Forum

    The number of ways of coming 8 and 9 are (2, 6), (3, 5), (4, 4), (5, 3), (6, 2), (3, 6), (4, 5), (5, 4), (6, 3) Total ways = 9
    So probability of coming 8 and 9 are

    =
    9
    =
    9
    6 × 636

    So probability of not coming these
    = 1 -
    9
    =
    3
    364

    Correct Option: D

    The number of ways of coming 8 and 9 are (2, 6), (3, 5), (4, 4), (5, 3), (6, 2), (3, 6), (4, 5), (5, 4), (6, 3) Total ways = 9
    So probability of coming 8 and 9 are

    =
    9
    =
    9
    6 × 636

    So probability of not coming these
    = 1 -
    9
    =
    3
    364


  1. A lot has 10% defective items. Ten items are chosen randomly from this lot. The probability that exactly 2 of the chosen items are defective is









  1. View Hint View Answer Discuss in Forum

    Probability of defective item =
    10
    = 0.1
    100

    Probability of not defective item = 1 – 0.1 = 0.9
    So, probability that exactly 2 of the chosen items are defective
    = 10C2 (0.1)² (0.9)8 = 0.1937.

    Correct Option: B

    Probability of defective item =
    10
    = 0.1
    100

    Probability of not defective item = 1 – 0.1 = 0.9
    So, probability that exactly 2 of the chosen items are defective
    = 10C2 (0.1)² (0.9)8 = 0.1937.



  1. From a pack of regular playing cards, two cards are drawn at random. What is the probability that both cards will be Kings, if first card in NOT replaced?









  1. View Hint View Answer Discuss in Forum

    Probability of both cards being king

    =
    4
    ×
    3
    =
    1

    5251221

    Correct Option: D

    Probability of both cards being king

    =
    4
    ×
    3
    =
    1

    5251221