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Probability Tes...

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  • Question 1
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    An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in a tail then a card from a well-shuffled pack of nine cards numbered $$1, 2, 3, .., 9$$ is randomly picked and the number on the card is noted. The probability that the noted number is either $$7$$ or $$8$$ is?

  • Question 2
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    If $$10$$ different balls are to be placed in $$4$$ distinct boxes at random, then the probability that two of these boxes contain exactly $$2$$ and $$3$$ balls is:

  • Question 3
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    An urn contains $$5$$ red and $$2$$ green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is :

  • Question 4
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    A random variable $$X$$ has the following probability distribution:

    $$X$$$$1$$$$2$$$$3$$$$4$$$$5$$
    $$P(X)$$$$k^{2}$$$$2k$$$$k$$$$2k$$$$5k^{2}$$
    Then $$P(X>2)$$ is equal to

  • Question 5
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    Two different families $$A$$ and $$B$$ are blessed with equal number of children. There are $$3$$ tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family $$B$$ is $$\displaystyle\dfrac{1}{12}$$, then the number of children in each family is?

  • Question 6
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    There are $$\mathrm{n}$$ urns each containing $$\mathrm{n}+1$$ balls such that the ith um contains $$\mathrm{i}$$ white balls and $$(\mathrm{n}+1-\mathrm{i})$$ red balls. Let $$\mathrm{u}_{\mathrm{i}}$$ be the event of selecting ith urn, $$\mathrm{i}=1,2,3\ldots,\ \mathrm{n}$$ and $$\mathrm{w}$$ denotes the event of getting a white ball.

    If $$\mathrm{n}$$ is even and $$\mathrm{E}$$ denotes the event of choosing even numbered um $$(\displaystyle \mathrm{P}(\mathrm{u}_{\mathrm{i}})=\frac{1}{\mathrm{n}})$$, then the value of $$\mathrm{P}(\mathrm{w}/\mathrm{E})$$ is 

  • Question 7
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    A box $$B_{1}$$ contains $$1$$ white ball, $$3$$ red balls and $$2$$ black balls. Another box $$B_{2}$$ contains $$2$$ white balls, $$3$$ red balls and $$4$$ black balls. A third box $$B_{3}$$ contains $$3$$ white balls, $$4$$ red balls and $$5$$ black balls.
    If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box $$B_{2}$$ is

  • Question 8
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    There are $$\mathrm{n}$$ urns each containing $$\mathrm{n}+1$$ balls such that the ith urn contains $$\mathrm{i}$$ white balls and $$(\mathrm{n}+1-\mathrm{i})$$ red balls. Let $$\mathrm{u}_{\mathrm{i}}$$ be the event of selecting ith urn, $$\mathrm{i}=1,2,3\ldots,\ \mathrm{n}$$ and $$\mathrm{w}$$ denotes the event of getting a white ball.

    $$\mathrm{I}\mathrm{f}\mathrm{P}(\mathrm{u}_{\mathrm{i}})=\mathrm{c}$$, where $$\mathrm{c}$$ is a constant then $$\mathrm{P}(\mathrm{u}_{\mathrm{n}}/\mathrm{w})$$ is equal to 

  • Question 9
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    One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is 

  • Question 10
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    A fair die is rolled repeatedly until a six is obtained. Let X denote the number of rolls required.
    The conditional probability that $$X \geq 6$$ given $$X > 3$$ equals

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