Total Questions:50 Total Time: 75 Min
Remaining:
Question:The probability of drawing a white ball from a bag containing 3 black balls and 4 white balls, is
\(\frac{4}{7}\)
\(\frac{3}{7}\)
\(\frac{1}{7}\)
None of these
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
5/8
1/2
1/3
2/3
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
\(\frac{{103}}{{2704}}\)
\(\frac{1}{{2704}}\)
\(\frac{2}{{52}}\)
\(\frac{{2601}}{{2704}}\)
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
\(\frac{3}{{16}}\)
\(\frac{5}{{16}}\)
\(\frac{{11}}{{16}}\)
\(\frac{{14}}{{16}}\)
Question:Two dice are thrown simultaneously. What is the probability of obtaining sum of the numbers less than 11
\(\frac{{17}}{{18}}\)
\(\frac{1}{{12}}\)
\(\frac{{11}}{{12}}\)
Question:The probability that an ordinary or a non-leap year has 53 sunday, is
\(\frac{2}{7}\)
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
\(\frac{1}{2}\)
\(\frac{3}{5}\)
\(\frac{1}{4}\)
\(\frac{1}{3}\)
Question:Two dice are tossed. The probability that the total score is a prime number is
\(\frac{1}{6}\)
\(\frac{5}{{12}}\)
Question:A card is drawn randomly from a pack of playing cards. Then the probability that it is neither ace nor king, is
\(\frac{{11}}{{13}}\)
\(\frac{8}{{13}}\)
\(\frac{{10}}{{13}}\)
\(\frac{{12}}{{13}}\)
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
\(\frac{{19}}{{24}}\)
\(\frac{{21}}{{23}}\)
\(\frac{{23}}{{24}}\)
\(\frac{1}{{24}}\)
Question:One card is drawn from a pack of 52 cards. The probability that it is a king or diamond is
\(\frac{1}{{26}}\)
\(\frac{3}{{26}}\)
\(\frac{4}{{13}}\)
\(\frac{3}{{13}}\)
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
\(\frac{2}{3}\)
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
\(\frac{{241}}{{1456}}\)
\(\frac{{164}}{{4165}}\)
\(\frac{{451}}{{884}}\)
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
\(\frac{4}{5}\)
\(\frac{2}{5}\)
\(\frac{7}{5}\)
\(\frac{9}{{25}}\)
Question:An integer is chosen at random and squared. The probability that the last digit of the square is 1 or 5 is
\(\frac{2}{{10}}\)
\(\frac{3}{{10}}\)
\(\frac{4}{{10}}\)
Question:Two integers are chosen at random and multiplied. The probability that the product is an even integer is
\(\frac{3}{4}\)
Question:Two cards are drawn without replacement from a well-shuffled pack. Find the probability that one of them is an ace of heart
\(\frac{1}{{25}}\)
\(\frac{1}{{52}}\)
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
Question:Probability of throwing 16 in one throw with three dice is
\(\frac{1}{{36}}\)
\(\frac{1}{{18}}\)
\(\frac{1}{{72}}\)
\(\frac{1}{9}\)
Question:The probability of choosing at random a number that is divisible by 6 or 8 from among 1 to 90 is equal to
\(\frac{1}{{30}}\)
\(\frac{{11}}{{80}}\)
\(\frac{{23}}{{90}}\)
Question:If Mohan has 3 tickets of a lottery containing 3 prizes and 9 blanks, then his chance of winning prize are
\(\frac{{34}}{{55}}\)
\(\frac{{21}}{{55}}\)
\(\frac{{17}}{{55}}\)
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
0
\(\frac{7}{{10}}\)
\(\frac{{10}}{{10}}\)
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
\(\frac{2}{n}\)
\(\frac{1}{n}\)
\(\frac{2}{{(n - 1)\,!}}\)
Question:A bag contains tickets numbered from 1 to 20. Two tickets are drawn. The probability that both the numbers are prime, is
\(\frac{{14}}{{95}}\)
\(\frac{7}{{95}}\)
\(\frac{1}{{95}}\)
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
\(\frac{1}{{45}}\)
\(\frac{1}{{90}}\)
\(\frac{1}{{100}}\)
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
\(\frac{1}{{84}}\)
\(\frac{1}{{21}}\)
\(\frac{5}{{84}}\)
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
\(\frac{2}{{801}}\)
\(\frac{2}{{623}}\)
\(\frac{1}{{267}}\)
\(\frac{1}{{623}}\)
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
\(\frac{{{}^8{C_6} \times {}^7{C_5}}}{{{}^{15}{C_{11}}}}\)
\(\frac{{^8{C_6}{ + ^7}{C_5}}}{{^{15}{C_{11}}}}\)
\(\frac{{15}}{{28}}\)
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
\(\frac{{14}}{{15}}\)
\(\frac{{11}}{{15}}\)
\(\frac{7}{{15}}\)
\(\frac{4}{{15}}\)
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
\(\frac{{21}}{{316}}\)
\(\frac{{19}}{{316}}\)
Question:A party of 23 persons take their seats at a round table. The odds against two persons sitting together are
10:01
1:11
9:10
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
Independent
Mutually exclusive
Mutually exclusive and independent
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)
0.9
0.1
0.2
0.3
Question:If A and B are two independent events, then \(P\,(A + B) = \)
\(P\,(A) + P\,(B) - P\,(A)\,P\,(B)\)
\(P\,(A) - P\,(B)\)
\(P\,(A) + P\,(B)\)
\(P\,(A) + P\,(B) + P\,(A)\,P\,(B)\)
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
60%
35%
25%
45%
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 \(P(A') + P(B') = \)
1.15
1.1
1.2
Question:If A and B are any two events, then \(P(\bar A \cap B) = \)
\(P(\bar A)\,\,\,P(\bar B)\)
\(1 - P(A) - P(B)\)
\(P(A) + P(B) - P(A \cap B)\)
\(P(B) - P(A \cap B)\)
Question:In two events \(P(A \cup B) = 5/6\), \(P({A^c}) = 5/6\), \(P(B) = 2/3,\) then A and B are
Mutually exhaustive
Dependent
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 \(P\,\left( {\frac{{\bar B}}{{\bar A}}} \right) = \)
\(\frac{{37}}{{40}}\)
\(\frac{{37}}{{45}}\)
\(\frac{{23}}{{40}}\)
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\(P\,\left( {\frac{A}{B}} \right) = \)
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
\(\frac{1}{{37}}\)
\(\frac{{36}}{{37}}\)
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 \(P\,\left( {\frac{E}{F}} \right) = \)
\(\frac{3}{8}\)
\(\frac{1}{8}\)
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
15
14
12
7
Question:If three dice are thrown together, then the probability of getting 5 on at least one of them is
\(\frac{{125}}{{216}}\)
\(\frac{{215}}{{216}}\)
\(\frac{1}{{216}}\)
\(\frac{{91}}{{216}}\)
Question:In a simultaneous toss of four coins, what is the probability of getting exactly three heads
Question:A coin is tossed successively three times. The probability of getting exactly one head or 2 heads, is
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
\({}^5{C_4}{\left( {\frac{4}{5}} \right)^4}\frac{1}{5}\)
\({\left( {\frac{4}{5}} \right)^4}\frac{1}{5}\)
\({}^5{C_1}\frac{1}{5}{\left( {\frac{4}{5}} \right)^4} \times {}^5{C_4}\)
Question:An experiment succeeds twice as often as it fails. Find the probability that in 4 trials there will be at least three success
\(\frac{4}{{27}}\)
\(\frac{8}{{27}}\)
\(\frac{{16}}{{27}}\)
\(\frac{{24}}{{27}}\)
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
Question:A dice is thrown two times. If getting the odd number is considered as success, then the probability of two successes is