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11.

Four numbers are chosen at random from{1, 2, 3, ..., 40}. The probability that they are not consecutive, is

$\frac{1}{2470}$

$\frac{4}{7969}$

$\frac{2469}{2470}$

$\frac{7965}{7969}$

12.

If A and B are mutually exclusive events with P(B) $\ne $ 1, then P(A$|$$\overline{)\mathrm{B}}$) is equal to(Here is the complement of the event B)

$\frac{1}{\mathrm{P}\left(\mathrm{B}\right)}$

$\frac{1}{1-\mathrm{P}\left(\mathrm{B}\right)}$

$\frac{\mathrm{P}\left(\mathrm{A}\right)}{\mathrm{P}\left(\mathrm{B}\right)}$

$\frac{\mathrm{P}\left(\mathrm{A}\right)}{1-\mathrm{P}\left(\mathrm{B}\right)}$

13.

Seven white balls and three black balls are randomly arranged in a row. The probability that no two black balls are placed adjacently is

$\frac{1}{2}$

$\frac{7}{15}$

$\frac{2}{15}$

$\frac{1}{3}$

14.

A student has to answer 10 out of 13 questions in an examination choosing atleast 5 questions from the first 6 questions. The number of choice available to the student is

63

91

161

196

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15.

A candidate takes three tests in succession and the probability of passing the first test is p. The probability of passing each succeeding test is p or $\frac{\mathrm{p}}{2}$ according as he passes or fails in the preceding one. The candidate is selected, if he passes atleast two tests. The probability that the candidate is selected, is

p

^{2}(2 - p)p(2 - p)

p + p

^{2}+ p^{3}p

^{2}(1 - p)

16.

Two persons A and B are throwing an unbiased six faced dice alternatively, with the condition that the person who throws 3 first wins the game. If A starts the game, then probabilities of A and B to win the same are, respectively

$\frac{6}{11},\frac{5}{11}$

$\frac{5}{11},\frac{6}{11}$

$\frac{8}{11},\frac{3}{11}$

$\frac{3}{11},\frac{8}{11}$

17.

3 out of 6 vertices of a regular hexagon are chosen at a time at random. The probability that the triangle formed with these three vertices is an equilateral triangle, is

$\frac{1}{2}$

$\frac{1}{5}$

$\frac{1}{10}$

$\frac{1}{20}$

18.

A bag P contains 5 white marbles and 3 black marbles. Four marbles are drawn at random from P and are put in an empty bag Q. If a marble drawn at random from Q is found to be black then the probability that all the three black marbles in P are transfered to the bag Q

$\frac{1}{7}$

$\frac{6}{7}$

$\frac{1}{8}$

$\frac{7}{8}$

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19.

There are 10 intermediate stations on a railway line between two particular stations. The number ofways that a train can be made to stop at 3 of these intermediate stations so that no two of these halting stations are consecutive is

56

20

126

120

20.

If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls, is

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