Probability Test 1

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?

A
$$\dfrac{13}{36}$$

B
$$\dfrac{19}{36}$$

C
$$\dfrac{19}{72}$$

D
$$\dfrac{15}{72}$$

Question 2
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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?

A
$$4$$

B
$$6$$

C
$$3$$

D
$$5$$

Question 3
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A box $$'A'$$ contains $$2$$ white, $$3$$ red and $$2$$ black balls. Another box $$'B'$$ contains $$4$$ white, $$2$$ red and $$3$$ black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box $$'B'$$ is

A
$$\dfrac {7}{16}$$

B
$$\dfrac {9}{32}$$

C
$$\dfrac {7}{8}$$

D
$$\dfrac {9}{16}$$

Question 4
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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

A
$$\displaystyle \frac{116}{181}$$

B
$$\displaystyle \frac{126}{181}$$

C
$$\displaystyle \frac{65}{181}$$

D
$$\displaystyle \frac{55}{181}$$

Question 5
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A computer producing factory has only two plants $${ T }_{ 1 }$$ and $$ { T }_{ 2 }$$. Plant $$ { T }_{ 1 }$$ produces $$20\%$$ and plant $${ T }_{ 2 }$$ produces $$80\%$$ of total computers produced. $$7\%$$ of computers produced in the factory turn out to be defective. It is known that $$P$$ (computer turns out to be defective given that it is produced in plant $${ T }_{ 1 }$$) $$=10P$$ (computer turns out to be defective given that it is produced in plant $$\displaystyle { T }_{ 2 }$$).
where $$P(E)$$ denotes the probability of an event $$E$$. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant $$ { T }_{ 2 }$$ is

A
$$\displaystyle \frac { 36 }{ 73 } $$

B
$$\displaystyle \frac { 47 }{ 79 } $$

C
$$\displaystyle \frac { 78 }{ 93 } $$

D
$$\displaystyle \frac { 75 }{ 83 } $$

Question 6
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A bag contains 12 balls out of which x are white.If one ball is drawn at random, what is the probability it will be a white ball?

A
$$ \displaystyle \frac{x}{2}$$

B
$$\displaystyle \frac{x}{12}$$

C
$$ \displaystyle \frac{x}{10}$$

D
$$ \displaystyle \frac{12}{x}$$

Question 7
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STATEMENT - 1 : Dependent events are those in which the outcome of one does not affect and is not affected by the other.
STATEMENT - 2 : Dependent events are those in which the outcome of one affects and is affected by the other.

A
Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1

B
Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1

C
Statement - 1 is True, Statement - 2 is False

D
Statement - 1 is False, Statement - 2 is True

Question 8
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All possible outcomes of a random experiment forms the -

A
Events

B
Sample space

C
Both

D
None of these

Question 9
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The sum of the probabilities of all the elementary events of an experiment is ____?

A
$$4$$

B
$$3$$

C
$$2$$

D
$$1$$

Question 10
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A bag contains 40 balls out of which some are red, some are blue and remaining are black. If the probability of drawing a red ball is $$\displaystyle \frac{11}{20}$$ and that of blue ball is $$\displaystyle \frac{1}{5}$$, then the number of black ball is?

A
$$5$$

B
$$25$$

C
$$10$$

D
$$30$$

Submit Test

Probability Tes...

Question 1

$$\dfrac{13}{36}$$

$$\dfrac{19}{36}$$

$$\dfrac{19}{72}$$

$$\dfrac{15}{72}$$

Question 2

$$4$$

$$6$$

$$3$$

$$5$$

Question 3

$$\dfrac {7}{16}$$

$$\dfrac {9}{32}$$

$$\dfrac {7}{8}$$

$$\dfrac {9}{16}$$

Question 4

$$\displaystyle \frac{116}{181}$$

$$\displaystyle \frac{126}{181}$$

$$\displaystyle \frac{65}{181}$$

$$\displaystyle \frac{55}{181}$$

Question 5

$$\displaystyle \frac { 36 }{ 73 } $$

$$\displaystyle \frac { 47 }{ 79 } $$

$$\displaystyle \frac { 78 }{ 93 } $$

$$\displaystyle \frac { 75 }{ 83 } $$

Question 6

$$ \displaystyle \frac{x}{2}$$

$$\displaystyle \frac{x}{12}$$

$$ \displaystyle \frac{x}{10}$$

$$ \displaystyle \frac{12}{x}$$

Question 7

Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1

Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1

Statement - 1 is True, Statement - 2 is False

Statement - 1 is False, Statement - 2 is True

Question 8

Events

Sample space

Both

None of these

Question 9

$$4$$

$$3$$

$$2$$

$$1$$

Question 10

$$5$$

$$25$$

$$10$$

$$30$$

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