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Probability Test - 10

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Probability Test - 10
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  • Question 1
    1 / -0.25

    A bag contains 6 white and 4 black balls. Two balls are drawn at random. Find the probability that they are of the same color.

    Solution

    It is given that a bag contains 6 white and 4 black balls and two balls are drawn at random.

    We know that, \({}^nC_r=\frac{n !}{r ! \times(n-r) !}\)

    Let S be the sample space. Then,

    Number of ways of drawing two balls out of 10 balls \({n(S)}={}^{10} \mathrm{C}_{2}\)

    \(\Rightarrow {n(S)}= \frac{10 !}{2 ! \times(10-2) !}\)

    \(\Rightarrow {n(S)}=\frac{10 !}{2 ! \times8 !}\)

    \(\Rightarrow {n(S)}=\frac{10 \times 9}{2 \times 1}=45\)

    Let E be the event of getting both balls of same color.

    Then, \(\mathrm{n}(\mathrm{E})=\) number of ways \((2\) balls out of \(6)\) or \((2\) balls out of 4\()\)

    \(\Rightarrow \mathrm{n}(\mathrm{E})={ }^{6} \mathrm{C}_{2}+{ }^{4} \mathrm{C}_{2}\)

    \(\Rightarrow \mathrm{n}(\mathrm{E})=\frac{6 !}{2 ! \times(6-2) !}+\frac{4 !}{2 ! \times(4-2) !}\)

    \(\Rightarrow \mathrm{n}(\mathrm{E})=\frac{6 !}{2 ! \times4 !}+\frac{4 !}{2 ! \times2 !}\)

    \(\Rightarrow \mathrm{n}(\mathrm{E})=\frac{6 \times 5}{2 \times 1}+\frac{4 \times 3}{2 \times 1}=15+6=21\)

    \(\therefore P(E)=\frac{n(E)}{n(S)}=\frac{21}{45}=\frac{7}{15}\)

    Hence, the correct option is (A).

  • Question 2
    1 / -0.25
    The probability of having 53 Mondays in a year is
  • Question 3
    1 / -0.25
    The probability that a card drawn from a pack of 52 cards will be a diamond or a king is
  • Question 4
    1 / -0.25
    A natural number is chosen at random from among the first 500. The probability of it being divisible by 3 or 5 is
  • Question 5
    1 / -0.25
    Three dice are thrown together. The probability of getting a total of at least 6 is
  • Question 6
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    The probability of getting more than seven when a pair of dice is thrown is
  • Question 7
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    A card is drawn at random from a pack of 52 cards. The probability of getting a red card or an ace is
  • Question 8
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    If a fair coin is tossed twice, what is the probability of getting heads in both the trials?
  • Question 9
    1 / -0.25
    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
  • Question 10
    1 / -0.25
    A bag contains 9 red and 6 white balls. Three balls are drawn at random. The probability that one ball is red and two balls are white is
  • Question 11
    1 / -0.25
    A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is
  • Question 12
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    Tickets numbered from 1 to 25 are mixed up together and a ticket is drawn at random. What is the probability that the drawn ticket has a prime number?
  • Question 13
    1 / -0.25
    A card is drawn from a well-shuffled pack of 52 cards. The probability of getting a queen of club or king of heart is
  • Question 14
    1 / -0.25
    A bag contains 8 white and 5 red balls. Three balls are drawn at random. What is the probability that all the drawn balls are white?
  • Question 15
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    The probability that a leap year selected at random will contain 53 Sundays is
  • Question 16
    1 / -0.25
    In a lottery of 50 tickets numbered 1 to 50, two tickets are drawn simultaneously. The probability that both the tickets drawn have prime numbers is
  • Question 17
    1 / -0.25
    Four cards are drawn at random from a pack of 52 cards. The probability of getting all the four cards of the same number is 
  • Question 18
    1 / -0.25
    N cadets have to stand in a row. If all possible permutations are equally likely, the probability of two particular cadets standing side by side is
  • Question 19
    1 / -0.25
    A bag contains 10 white, 4 green balls. One ball is drawn at random. The probability that it is white is
  • Question 20
    1 / -0.25
    In a simultaneous throw of two dice, the probability of getting a total of 7 is
  • Question 21
    1 / -0.25
    Two cards are drawn from a pack. The probability of getting a king and a queen is
  • Question 22
    1 / -0.25
    Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random. What is the probability that the drawn ticket has a number which is a multiple of 3 or 7?
  • Question 23
    1 / -0.25
    A bag contains 6 black, 9 white and 5 red balls. Three balls are drawn at random. What is the probability that the balls drawn are black?
  • Question 24
    1 / -0.25
    A pair of dice is thrown and the numbers appearing have sum greater than or equal to 10. The probability of getting a sum of 10 is
  • Question 25
    1 / -0.25
    In a collection of 6 Mathematics and 4 Physics books, the probability that 3 particular Mathematics books will be together, is
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