Probability Test

Result

Probability Test - 57

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Weekly Quiz Competition

Question 1
1 / -0

A subset A of X =$${1,2,3,.......,100}$$ is chosen at random. The set X is reconstructed by replacing by elements of A and another subset B of X is chosen at random. The probability that A $$\cap$$ B contains exactly $$10$$ elements is

A
$$\dfrac{1}{10}$$

B
$$^{100}C_{10} (\dfrac{1}{2})^{100}$$

C
$$^{100}C_{10} (\dfrac{1}{4})^{100}$$

D
$$^{100}C_{10} \dfrac{3^{90}}{4^{100}}$$

Solution
Question 2
1 / -0

A candidate is required to answer 6 questions by choosing at least one question from each section, where 1st section consists of 5 questions, 2nd section consists of 3rd questions and 3rd section consists of 2 questions. In how many ways can he make up his choice?

A
225

B
320

C
175

D
200

Solution
Question 3
1 / -0

Two players $${P}_{1}$$ and $${P}_{2}$$ play a series of $$2n$$ games. Each game can be result in either a win or lose for $${P}_{1}$$. Total numbers of ways in which $${P}_{1}$$ can win the series of these games is equal to

A
$$\dfrac{1}{3}({ 2 }^{ 2n }-2^{ 2n }{ C }_{ n })$$

B
$$\dfrac{1}{2}({ 2 }^{ 2n }-^{ 2n }{ C }_{ n })$$

C
$$\dfrac{1}{3}({ 2 }^{ n }-2^{ 2n }{ C }_{ n })$$

D
$$\dfrac{{ 2 }^{ 2n }-2^{ 2n }{ C }_{ n }}{2}$$
Question 4
1 / -0

Players A has 2 fair coins and B has one more coin than the players A. Both the players throw all of their coins simultaneously and observe the number that come up heads.Assuming that all coins are fairs, the probability that B obtains more heads than A, is

A
$$\frac{{16}}{{32}}$$

B
$$\frac{{18}}{{32}}$$

C
$$\frac{{13}}{{32}}$$

D
$$\frac{{12}}{{32}}$$

Solution
Question 5
1 / -0

There are two bags.One bag contains $$4$$ white and $$2$$ black balls. Second bag contains $$5$$ white and $$4$$ black balls. Two balls are transferred from first bag to second bag . Then one ball it taken from the second bag. Find the probability that it is white.

A
$$\dfrac{18}{33}$$

B
$$\dfrac {19}{ 33}$$

C
$$\dfrac {20}{33}$$

D
$$\dfrac {19}{34}$$

Solution
Question 6
1 / -0

If $$P (A \cup B) = 10P (A \cap B)$$ and $$P(B) = 2P(A)$$ then $$P \left(\dfrac{B}{A}\right)$$ is equal to-

A
$$\dfrac{1}{11}$$

B
$$\dfrac{2}{11}$$

C
$$\dfrac{3}{11}$$

D
$$\dfrac{4}{11}$$

Solution
Question 7
1 / -0

For the following probability distribution.
$$X=x$$ $$1$$ $$0$$ $$4$$
P $$1/2$$ $$3/8$$ $$1/8$$
The value of $$E[X-E(X)]$$ is?

A
$$1$$

B
$$1/2$$

C
$$0$$

D
$$1/4$$
Question 8
1 / -0

If from a pack of $$52$$ well shuffled cards, cards are drawn one by without replacement and the third card is found to be ACE. What is the probability that first two cards are not ACES?

A
$$\dfrac{260}{329}$$

B
$$\dfrac{376}{425}$$

C
$$\dfrac{161}{329}$$

D
None of these

Solution
Question 9
1 / -0

A man and a woman appear in an interview for two vacancies in the same post. The probability of man's selection is 1/4 and that of the woman's selection is $$\dfrac { 1 }{ 3 } $$. What is the probability that none of them will be selected.

A
$$\dfrac { 1 }{ 2 } $$

B
$$\dfrac { 1 }{ 3 } $$

C
$$\dfrac { 1 }{ 4 } $$

D
$$\dfrac { 1 }{ 8 } $$
Question 10
1 / -0

A and B alternately throw a pair of the die until one of them wins. A is considered winner if he gets a total 7 and B is considered winner if he gets a total of 5. If A starts the game, then the probability that one of the die shows face 3 on the last throw is -

A
$$\dfrac{11}{28}$$

B
$$\dfrac{9}{28}$$

C
$$\dfrac{5}{28}$$

D
$$\dfrac{3}{28}$$

Solution