Probability Test 4

Total Questions:50 Total Time: 75 Min

Remaining:

 

Questions 1 of 50

Question:The probability of drawing a white ball from a bag containing 3 black balls and 4 white balls, is

Answers Choices:

\(\frac{4}{7}\)

\(\frac{3}{7}\)

\(\frac{1}{7}\)

None of these

Questions 2 of 50

Question:A and B toss a coin alternatively, the first to show a head being the winner. If A starts the game, the chance of his winning is

Answers Choices:

5/8

1/2

1/3

2/3

Questions 3 of 50

Question:One card is drawn from each of two ordinary packs of 52 cards. The probability that at least one of them is an ace of heart, is

Answers Choices:

\(\frac{{103}}{{2704}}\)

\(\frac{1}{{2704}}\)

\(\frac{2}{{52}}\)

\(\frac{{2601}}{{2704}}\)

Questions 4 of 50

Question:A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, what is the probability that it is rusted or is a nail

Answers Choices:

\(\frac{3}{{16}}\)

\(\frac{5}{{16}}\)

\(\frac{{11}}{{16}}\)

\(\frac{{14}}{{16}}\)

Questions 5 of 50

Question:Two dice are thrown simultaneously. What is the probability of obtaining sum of the numbers less than 11

Answers Choices:

\(\frac{{17}}{{18}}\)

\(\frac{1}{{12}}\)

\(\frac{{11}}{{12}}\)

None of these

Questions 6 of 50

Question:The probability that an ordinary or a non-leap year has 53 sunday, is

Answers Choices:

\(\frac{2}{7}\)

\(\frac{1}{7}\)

\(\frac{3}{7}\)

None of these

Questions 7 of 50

Question:A coin is tossed until a head appears or until the coin has been tossed five times. If a head does not occur on the first two tosses, then the probability that the coin will be tossed 5 times is

Answers Choices:

\(\frac{1}{2}\)

\(\frac{3}{5}\)

\(\frac{1}{4}\)

\(\frac{1}{3}\)

Questions 8 of 50

Question:Two dice are tossed. The probability that the total score is a prime number is

Answers Choices:

\(\frac{1}{6}\)

\(\frac{5}{{12}}\)

\(\frac{1}{2}\)

None of these

Questions 9 of 50

Question:A card is drawn randomly from a pack of playing cards. Then the probability that it is neither ace nor king, is

Answers Choices:

\(\frac{{11}}{{13}}\)

\(\frac{8}{{13}}\)

\(\frac{{10}}{{13}}\)

\(\frac{{12}}{{13}}\)

Questions 10 of 50

Question:There are 4 envelopes with addresses and 4 concerning letters. The probability that letter does not go into concerning proper envelope, is or There are four letters and four addressed envelopes. The chance that all letters are not despatched in the right envelope is

Answers Choices:

\(\frac{{19}}{{24}}\)

\(\frac{{21}}{{23}}\)

\(\frac{{23}}{{24}}\)

\(\frac{1}{{24}}\)

Questions 11 of 50

Question:One card is drawn from a pack of 52 cards. The probability that it is a king or diamond is

Answers Choices:

\(\frac{1}{{26}}\)

\(\frac{3}{{26}}\)

\(\frac{4}{{13}}\)

\(\frac{3}{{13}}\)

Questions 12 of 50

Question:A bag contains 3 white, 3 black and 2 red balls. One by one three balls are drawn without replacing them. The probability that the third ball is red, is

Answers Choices:

\(\frac{1}{2}\)

\(\frac{1}{3}\)

\(\frac{2}{3}\)

\(\frac{1}{4}\)

Questions 13 of 50

Question:Cards are drawn one by one without replacement from a pack of 52 cards. The probability that 10 cards will precede the first ace is

Answers Choices:

\(\frac{{241}}{{1456}}\)

\(\frac{{164}}{{4165}}\)

\(\frac{{451}}{{884}}\)

None of these

Questions 14 of 50

Question:The probability that a teacher will give an unannounced test during any class meeting is 1/5. If a student is absent twice, then the probability that the student will miss at least one test is

Answers Choices:

\(\frac{4}{5}\)

\(\frac{2}{5}\)

\(\frac{7}{5}\)

\(\frac{9}{{25}}\)

Questions 15 of 50

Question:An integer is chosen at random and squared. The probability that the last digit of the square is 1 or 5 is

Answers Choices:

\(\frac{2}{{10}}\)

\(\frac{3}{{10}}\)

\(\frac{4}{{10}}\)

\(\frac{9}{{25}}\)

Questions 16 of 50

Question:Two integers are chosen at random and multiplied. The probability that the product is an even integer is

Answers Choices:

\(\frac{1}{2}\)

\(\frac{2}{3}\)

\(\frac{3}{4}\)

\(\frac{4}{5}\)

Questions 17 of 50

Question:Two cards are drawn without replacement from a well-shuffled pack. Find the probability that one of them is an ace of heart

Answers Choices:

\(\frac{1}{{25}}\)

\(\frac{1}{{26}}\)

\(\frac{1}{{52}}\)

None of these

Questions 18 of 50

Question:A problem in Mathematics is given to three students A, B, C and their respective probability of solving the problem is 1/2, 1/3 and 1/4. Probability that the problem is solved is

Answers Choices:

\(\frac{3}{4}\)

\(\frac{1}{2}\)

\(\frac{2}{3}\)

\(\frac{1}{3}\)

Questions 19 of 50

Question:Probability of throwing 16 in one throw with three dice is

Answers Choices:

\(\frac{1}{{36}}\)

\(\frac{1}{{18}}\)

\(\frac{1}{{72}}\)

\(\frac{1}{9}\)

Questions 20 of 50

Question:The probability of choosing at random a number that is divisible by 6 or 8 from among 1 to 90 is equal to

Answers Choices:

\(\frac{1}{6}\)

\(\frac{1}{{30}}\)

\(\frac{{11}}{{80}}\)

\(\frac{{23}}{{90}}\)

Questions 21 of 50

Question:If Mohan has 3 tickets of a lottery containing 3 prizes and 9 blanks, then his chance of winning prize are

Answers Choices:

\(\frac{{34}}{{55}}\)

\(\frac{{21}}{{55}}\)

\(\frac{{17}}{{55}}\)

None of these

Questions 22 of 50

Question:A bag contains 3 white and 7 red balls. If a ball is drawn at random, then what is the probability that the drawn ball is either white or red

Answers Choices:

0

\(\frac{3}{{10}}\)

\(\frac{7}{{10}}\)

\(\frac{{10}}{{10}}\)

Questions 23 of 50

Question:n cadets have to stand in a row. If all possible permutations are equally likely, then the probability that two particular cadets stand side by side, is

Answers Choices:

\(\frac{2}{n}\)

\(\frac{1}{n}\)

\(\frac{2}{{(n - 1)\,!}}\)

None of these

Questions 24 of 50

Question:A bag contains tickets numbered from 1 to 20. Two tickets are drawn. The probability that both the numbers are prime, is

Answers Choices:

\(\frac{{14}}{{95}}\)

\(\frac{7}{{95}}\)

\(\frac{1}{{95}}\)

None of these

Questions 25 of 50

Question:Dialing a telephone number an old man forgets the last two digits remembering only that these are different dialled at random. The probability that the number is dialled correctly, is

Answers Choices:

\(\frac{1}{{45}}\)

\(\frac{1}{{90}}\)

\(\frac{1}{{100}}\)

None of these

Questions 26 of 50

Question:In a box there are 2 red, 3 black and 4 white balls. Out of these three balls are drawn together. The probability of these being of same colour is

Answers Choices:

\(\frac{1}{{84}}\)

\(\frac{1}{{21}}\)

\(\frac{5}{{84}}\)

None of these

Questions 27 of 50

Question:In a lottery there were 90 tickets numbered 1 to 90. Five tickets were drawn at random. The probability that two of the tickets drawn numbers 15 and 89 is

Answers Choices:

\(\frac{2}{{801}}\)

\(\frac{2}{{623}}\)

\(\frac{1}{{267}}\)

\(\frac{1}{{623}}\)

Questions 28 of 50

Question:Among 15 players, 8 are batsmen and 7 are bowlers. Find the probability that a team is chosen of 6 batsmen and 5 bowlers

Answers Choices:

\(\frac{{{}^8{C_6} \times {}^7{C_5}}}{{{}^{15}{C_{11}}}}\)

\(\frac{{^8{C_6}{ + ^7}{C_5}}}{{^{15}{C_{11}}}}\)

\(\frac{{15}}{{28}}\)

None of these

Questions 29 of 50

Question:A bag contains 8 red and 7 black balls. Two balls are drawn at random. The probability that both the balls are of the same colour is

Answers Choices:

\(\frac{{14}}{{15}}\)

\(\frac{{11}}{{15}}\)

\(\frac{7}{{15}}\)

\(\frac{4}{{15}}\)

Questions 30 of 50

Question:From eighty cards numbered 1 to 80, two cards are selected randomly. The probability that both the cards have the numbers divisible by 4 is given by

Answers Choices:

\(\frac{{21}}{{316}}\)

\(\frac{{19}}{{316}}\)

\(\frac{1}{4}\)

None of these

Questions 31 of 50

Question:A party of 23 persons take their seats at a round table. The odds against two persons sitting together are

Answers Choices:

10:01

1:11

9:10

None of these

Questions 32 of 50

Question:If two events A and B are such that \(P\,(A + B) = \frac{5}{6},\) \(P\,(AB) = \frac{1}{3}\,\)and \(P\,(\bar A) = \frac{1}{2},\) then the events A and B are

Answers Choices:

Independent

Mutually exclusive

Mutually exclusive and independent

None of these

Questions 33 of 50

Question:If A and B are two independent events such that \(P\,(A) = 0.40,\,\,P\,(B) = 0.50.\) Find \(P\)(neither A nor B)

Answers Choices:

0.9

0.1

0.2

0.3

Questions 34 of 50

Question:If A and B are two independent events, then \(P\,(A + B) = \)

Answers Choices:

\(P\,(A) + P\,(B) - P\,(A)\,P\,(B)\)

\(P\,(A) - P\,(B)\)

\(P\,(A) + P\,(B)\)

\(P\,(A) + P\,(B) + P\,(A)\,P\,(B)\)

Questions 35 of 50

Question:In a city 20% persons read English newspaper, 40% read Hindi newspaper and 5% read both newspapers. The percentage of non-reader either paper is

Answers Choices:

60%

35%

25%

45%

Questions 36 of 50

Question:The probability that at least one of A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, then \(P(A') + P(B') = \)

Answers Choices:

0.9

1.15

1.1

1.2

Questions 37 of 50

Question:If A and B are any two events, then \(P(\bar A \cap B) = \)

Answers Choices:

\(P(\bar A)\,\,\,P(\bar B)\)

\(1 - P(A) - P(B)\)

\(P(A) + P(B) - P(A \cap B)\)

\(P(B) - P(A \cap B)\)

Questions 38 of 50

Question:In two events \(P(A \cup B) = 5/6\), \(P({A^c}) = 5/6\), \(P(B) = 2/3,\) then A and B are

Answers Choices:

Independent

Mutually exclusive

Mutually exhaustive

Dependent

Questions 39 of 50

Question:If A and B are two events such that \(P\,(A) = \frac{1}{3}\), \(P\,(B) = \frac{1}{4}\) and \(P\,(A \cap B) = \frac{1}{5},\) then \(P\,\left( {\frac{{\bar B}}{{\bar A}}} \right) = \)

Answers Choices:

\(\frac{{37}}{{40}}\)

\(\frac{{37}}{{45}}\)

\(\frac{{23}}{{40}}\)

None of these

Questions 40 of 50

Question:If A and B are two events such that \(P\,(A) = \frac{3}{8},\,\) \(P\,(B) = \frac{5}{8}\) and \(P\,(A \cup B) = \frac{3}{4},\) then\(P\,\left( {\frac{A}{B}} \right) = \)

Answers Choices:

\(\frac{2}{5}\)

\(\frac{2}{3}\)

\(\frac{3}{5}\)

None of these

Questions 41 of 50

Question:In an entrance test there are multiple choice questions. There are four possible answers to each question of which one is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then the probability that he was guessing, is

Answers Choices:

\(\frac{{37}}{{40}}\)

\(\frac{1}{{37}}\)

\(\frac{{36}}{{37}}\)

\(\frac{1}{9}\)

Questions 42 of 50

Question:A coin is tossed three times in succession. If E is the event that there are at least two heads and F is the event in which first throw is a head, then \(P\,\left( {\frac{E}{F}} \right) = \)

Answers Choices:

\(\frac{3}{4}\)

\(\frac{3}{8}\)

\(\frac{1}{2}\)

\(\frac{1}{8}\)

Questions 43 of 50

Question:A fair coin is tossed n times. If the probability that head occurs 6 times is equal to the probability that head occurs 8 times, then n is equal to

Answers Choices:

15

14

12

7

Questions 44 of 50

Question:If three dice are thrown together, then the probability of getting 5 on at least one of them is

Answers Choices:

\(\frac{{125}}{{216}}\)

\(\frac{{215}}{{216}}\)

\(\frac{1}{{216}}\)

\(\frac{{91}}{{216}}\)

Questions 45 of 50

Question:In a simultaneous toss of four coins, what is the probability of getting exactly three heads

Answers Choices:

\(\frac{1}{2}\)

\(\frac{1}{3}\)

\(\frac{1}{4}\)

None of these

Questions 46 of 50

Question:A coin is tossed successively three times. The probability of getting exactly one head or 2 heads, is

Answers Choices:

\(\frac{1}{4}\)

\(\frac{1}{2}\)

\(\frac{3}{4}\)

None of these

Questions 47 of 50

Question:The probability that a student is not a swimmer is 1/5. What is the probability that out of 5 students, 4 are swimmers

Answers Choices:

\({}^5{C_4}{\left( {\frac{4}{5}} \right)^4}\frac{1}{5}\)

\({\left( {\frac{4}{5}} \right)^4}\frac{1}{5}\)

\({}^5{C_1}\frac{1}{5}{\left( {\frac{4}{5}} \right)^4} \times {}^5{C_4}\)

None of these

Questions 48 of 50

Question:An experiment succeeds twice as often as it fails. Find the probability that in 4 trials there will be at least three success

Answers Choices:

\(\frac{4}{{27}}\)

\(\frac{8}{{27}}\)

\(\frac{{16}}{{27}}\)

\(\frac{{24}}{{27}}\)

Questions 49 of 50

Question:A coin is tossed 3 times. The probability of obtaining at least two heads is or Three coins are tossed all together. The probability of getting at least two heads is

Answers Choices:

\(\frac{1}{8}\)

\(\frac{3}{8}\)

\(\frac{1}{2}\)

\(\frac{2}{3}\)

Questions 50 of 50

Question:A dice is thrown two times. If getting the odd number is considered as success, then the probability of two successes is

Answers Choices:

\(\frac{1}{2}\)

\(\frac{3}{4}\)

\(\frac{2}{3}\)

\(\frac{1}{4}\)