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Quiz: Probability

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Number of Questions: 27

Question: 16 -

What is the probability of getting the sum as a prime number if two dice are thrown?

Options:

  1. 5/24

  2. 1/4

  3. 5/12

  4. 5/30

    5. Answer:

    5/12
    Solution:

    As per the question: n (S) = 6*6 = 36

    And, the event that the sum is a prime number:

    E = {(1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3),

    (5, 2), (5, 6), (6, 1), (6, 5)}

    So, n (E) = 15

    n(E) / n(S) = 15/36 = 5/12

Question: 17 -

The probability of getting two tails when two coins are tossed is -

Options:

  1. 1/2

  2. 1/6

  3. 1/3

  4. 1/4

    5. Answer:

    1/4
    Solution:

    The sample space when two coins are tossed = (H, H), (H, T), (T, H), (T, T)

    So, n(S) = 4

    The event "E" of getting two tails (T, T) = 1

    So, n(E) = 1

    So, the probability of getting two tails, P (E) = n(E) / n(S) = 1/4

Question: 18 -

If two dice are thrown together, what is the probability of getting an even number on one dice and an odd number on the other dice?

Options:

  1. 3/5

  2. 1/2

  3. 1/4

  4. 3/4

    5. Answer:

    1/2
    Solution:

    n (S) = 6*6 = 36

    Let E be the event of getting an even number on one die and an odd number on the other

    E = {( (1,2) (1,4) (1,6) (2,1) (2,3) (2,5) (3,2) (3,4) (3,6) (4,1) (4,3) (4,5) (5,2) (5,4) (5,6) (6,1) (6,3) (6,5)}

    So, n (E) = 18

    n(E) / n(S) = 18/36 = 1/2

Question: 19 -

A dice is thrown twice. What is the probability of getting two numbers whose product is even?

Options:

  1. 6/4

  2. 5/4

  3. 3/4

  4. 1/2

    5. Answer:

    3/4
    Solution:

    In a simultaneous throw of the two dice, the sample space, S = 6 * 6 = 36

    So, n (S) = 36

    The event "E" = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

    So, n (E) = 27

    P(E) = n(E)/n(S) = 27/36 = 3/4

Question: 20 -

Suppose a number x is chosen from the numbers -2, -1, 0, 1, 2. What will be the probability of x2 > 0?

Options:

  1. 3/5

  2. 1/5

  3. 4/5

  4. 2/3

    5. Answer:

    4/5
    Solution:

    The numbers given in the question are -2, -1, 0, 1, 2.

    The squares of these numbers are 4, 1, 0, 1, 4. So the square of four numbers is greater than 0.

    Therefore, the probability of x2 > 0 is 4/5.