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Quiz: Probability

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Number of Questions: 27

Question: 6 -

What is the probability of getting 53 Mondays in a leap year?

Options:

  1. 1/7

  2. 53/366

  3. 7/366

  4. 2/7

    5. Answer:

    2/7
    Solution:

    With 366 days, the number of weeks in a year is

    366/7 = 52 (2/7)

    i.e., 52 complete weeks which contains 52 Mondays,

    Now 2 days of the year are remaining.

    These two days can be

    (Sunday, Monday), (Monday, Tuesday), (Tuesday, Wednesday), (Wednesday, Thursday), (Thursday, Friday), (Friday, Saturday), (Saturday, Sunday)

    i.e., there are 7 pairs, in which Monday occurs in 2 pairs,

    So probability is:

    P (53 Monday) = 2/7

Question: 7 -

A box of 600 bulbs contains 12 defective bulbs. One bulb is taken out at random from this box. Then the probability that it is non-defective bulb is:

Options:

  1. 143/150

  2. 1/25

  3. 147/150

  4. 1/50

    5. Answer:

    147/150
    Solution:

    P (non-defective bulb) = 1 – P (Defective bulb)

    = 1 – (12/600)

    = (600 – 12)/600

    = 588/600

    = 147/150

Question: 8 -

Cards marked with numbers 2 to 101 are placed in a box and mixed thoroughly. One card is drawn from this box randomly, then the probability that the number on card is a perfect square.

Options:

  1. 9/100

  2. 19/100

  3. 1/10

  4. 3/10

    5. Answer:

    1/10
    Solution:

    The perfect square numbers between 2 to 101 are:

    1, 4, 9, 16, 25, 36, 49, 64, 81, 100

    Total numbers from 2 to 101 =100

    So probability of getting a card with perfect square number is:

    P (perfect square) = 10/100

    ⇒ P (perfect square) = 1/10

Question: 9 -

A card is drawn from a well shuffled deck of 52 cards. Find the probability of getting a king of red suit.

Options:

  1. 3/26

  2. 7/52

  3. 1/26

  4. 1/13

    5. Answer:

    1/26
    Solution:

    There are total 4 kings in 52 cards, 2 of red colour and 2 of black colour

    Therefore, Probability of getting a king of red suit is:

    P (King of red suit) = 2/52

    ⇒ P (King of red suit) = 1/26

Question: 10 -

A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number 1,2,3……12 ,then the probability that it will point to an odd number is:

Options:

  1. 1/6

  2. 1/12

  3. 7/12

  4. 5/12

    5. Answer:

    1/6
    Solution:

    The odd numbers in 1,2,3……..12 are:

    1,3,5,7,9,11

    Therefore probability that an odd number will come is:

    P (odd number) = 6/12

    ⇒ P (odd number) = 1/2