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Quiz: Probability

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Number of Questions: 27

Question: 21 -

In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:

Options:

  1. 25/117

  2. 3/25

  3. 21/46

  4. 1/50

    5. Answer:

    21/46
    Solution:

    Let S be the sample space and E be the event of selecting 1 girl and 2 boys.

    Then, n(S) = Number ways of selecting 3 students out of 25
      = 25C3 `
     
    = (25 x 24 x 23)/
    (3 x 2 x 1)
      = 2300.
    n(E) = (10C1 x 15C2)
     
    = 10 x (15 x 14)/
    (2 x 1)
      = 1050.
     P(E) = n(E)/ = 1050/ = 21/ .
    n(S) 2300 46

Question: 22 -

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?

Options:

  1. 51/91

  2. 33/91

  3. 65/91

  4. 17/91

    5. Answer:

    33/91
    Solution:

    Three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91

Question: 23 -

What is the probability of the random arrangement of letters in the word "UNIVERSITY" and two I's should come together?

Options:

  1. 3/5

  2. 1/7

  3. 1/5

  4. 2/7

    5. Answer:

    1/5
    Solution:

    The total number of words that can be formed using the letters of the word "UNIVERSITY" and the two I's should come together is = 10!/2!

    If we consider two I's as one letter, the number of ways of arrangement in which both I's are together = 9!

    The required probability is = 9!/10!/2! = 2/10 = 1/5

Question: 24 -

The probability of each event, when a coin is tossed 100 times with frequencies: head 40 and tail 60 is

Options:

  1. 0.20 & 0.80

  2. 0.50 & 0.50

  3. 0.40 & 0.60

  4. 0.60 & 0.40

    5. Answer:

    0.40 & 0.60
    Solution:

    Suppose A and B are the events of the occurrence of head and tail, respectively.

    Probability of Occurrence of Head P (A) = Number of heads/Total number of possible outcomes

    P (E) = 40/100 = 0.40

    Similarly, P (B) = No of tails/ Total number of possible outcomes

    P (B) = 60/100 = 0.60

    Hence, the values of heads and tails are 0.40 & 0.60.

Question: 25 -

In a class, 30% of students study Hindi, 45% study Maths, and 15% study both Hindi and Maths. If a student is randomly selected, what is the probability that he/she study Hindi or Maths?

Options:

  1. 2/5

  2. 3/5

  3. 1/5

  4. 2/7

    5. Answer:

    3/5
    Solution:

    Given that 45% study Hindi, i.e., P(H) = 45/100 = 9/20

    30% study Maths, i.e., P(M) = 30/100 = 6/20

    15% study both Hindi and Maths, i.e., P(H and M) = 15/100 = 3/20

    So, P(H or M) = P(H) + P(M) - P(H and M)

    = 9/20 + 6/20 - 3/20

    = 12/20 or 3/5