Total Questions:50 Total Time: 75 Min
Remaining:
Question:Two card are drawn successively with replacement from a pack of 52 cards. The probability of drawing two aces is
\(\frac{1}{{169}}\)
\(\frac{1}{{221}}\)
\(\frac{1}{{2652}}\)
\(\frac{4}{{663}}\)
Question:In a single throw of two dice, the probability of getting more than 7 is
\(\frac{7}{{36}}\)
\(\frac{7}{{12}}\)
\(\frac{5}{{12}}\)
\(\frac{5}{{36}}\)
Question:A dice is thrown twice. The probability of getting 4, 5 or 6 in the first throw and 1, 2, 3 or 4 in the second throw is
1
\(\frac{1}{3}\)
None of these
Question:Two cards are drawn from a pack of 52 cards. What is the probability that at least one of the cards drawn is an ace
\(\frac{{33}}{{221}}\)
\(\frac{{188}}{{221}}\)
\(\frac{1}{{26}}\)
\(\frac{{21}}{{221}}\)
Question:In a simultaneous throw of three coins, what is the probability of getting at least 2 tails
\(\frac{1}{8}\)
\(\frac{1}{4}\)
\(\frac{1}{2}\)
Question:In a throw of a die, what is the probability of getting a number less than 7
0
Question:A box contains 10 good articles and 6 with defects. One article is chosen at random. What is the probability that it is either good or has a defect
\(\frac{{24}}{{64}}\)
\(\frac{{40}}{{64}}\)
\(\frac{{49}}{{64}}\)
\(\frac{{64}}{{64}}\)
Question:The probability of happening of an impossible event i.e. \(P\,(\varphi )\) is
2
Question:A number is chosen from first 100 natural numbers. The probability that the number is even or divisible by 5, is
\(\frac{3}{4}\)
\(\frac{2}{3}\)
\(\frac{4}{5}\)
\(\frac{3}{5}\)
Question:Two dice are thrown. If first shows 5, then the probability that the sum of the numbers appears on both is 8 or more than 8, is
\(\frac{1}{{12}}\)
\(\frac{{11}}{{12}}\)
Question:The probability of hitting a target by three marksmen are \(\frac{1}{2},\,\frac{1}{3}\) and \(\frac{1}{4}\) respectively. The probability that one and only one of them will hit the target when they fire simultaneously, is
\(\frac{{11}}{{24}}\)
Question:A determinant is chosen at random. The set of all determinants of order 2 with elements 0 or 1 only. The probability that value of the determinant chosen is positive, is
3/16
3/8
1/4
Question:A box contains 2 black, 4 white and 3 red balls. One ball is drawn at random from the box and kept aside. From the remaining balls in the box, another ball is drawn at random and kept aside the first. This process is repeated till all the balls are drawn from the box. The probability that the balls drawn are in the sequence of 2 black, 4 white and 3 red is
\(\frac{1}{{1260}}\)
\(\frac{1}{{7560}}\)
\(\frac{1}{{126}}\)
Question:A dice is rolled three times, the probability of getting a larger number than the previous number each time is
\(\frac{{15}}{{216}}\)
\(\frac{5}{{54}}\)
\(\frac{{13}}{{216}}\)
\(\frac{1}{{18}}\)
Question:The sum of two positive numbers is 100. The probability that their product is greater than 1000 is
\(\frac{7}{9}\)
\(\frac{7}{{10}}\)
\(\frac{2}{5}\)
Question:The corners of regular tetrahedrons are numbered 1, 2, 3, 4. Three tetrahedrons are tossed. The probability that the sum of upward corners will be 5 is
\(\frac{5}{{24}}\)
\(\frac{5}{{64}}\)
\(\frac{3}{{32}}\)
\(\frac{3}{{16}}\)
Question:The probability that a leap year will have 53 Fridays or 53 Saturdays is
\(\frac{2}{7}\)
\(\frac{3}{7}\)
\(\frac{4}{7}\)
\(\frac{1}{7}\)
Question:Find the probability that the two digit number formed by digits 1, 2, 3, 4, 5 is divisible by 4 (while repetition of digit is allowed)
\(\frac{1}{{30}}\)
\(\frac{1}{{20}}\)
\(\frac{1}{{40}}\)
Question:"X" speaks truth in 60% and "Y" in 50% of the cases. The probability that they contradict each other narrating the same incident is
Question:The probability that A speaks truth is \(\frac{4}{5}\), while this probability for B is \(\frac{3}{4}\). The probability that they contradict each other when asked to speak on a fact
\(\frac{1}{5}\)
\(\frac{7}{{20}}\)
\(\frac{3}{{20}}\)
Question:A word consists of 11 letters in which there are 7 consonants and 4 vowels. If 2 letters are chosen at random, then the probability that all of them are consonants, is
\(\frac{5}{{11}}\)
\(\frac{{21}}{{55}}\)
\(\frac{4}{{11}}\)
Question:Twenty tickets are marked the numbers 1, 2, ..... 20. If three tickets be drawn at random, then what is the probability that those marked 7 and 11 are among them
\(\frac{3}{{190}}\)
\(\frac{1}{{19}}\)
\(\frac{1}{{190}}\)
Question:An ordinary cube has four blank faces, one face marked 2 another marked 3. Then the probability of obtaining a total of exactly 12 in 5 throws, is
\(\frac{5}{{1296}}\)
\(\frac{5}{{1944}}\)
\(\frac{5}{{2592}}\)
Question:Two persons each make a single throw with a die. The probability they get equal value is\({p_1}\). Four persons each make a single throw and probability of three being equal is\({p_2}\), then
\({p_1} = {p_2}\)
\({p_1} < {p_2}\)
\({p_1} > {p_2}\)
Question:Two numbers a and b are chosen at random from the set of first 30 natural numbers. The probability that \({a^2} - {b^2}\)is divisible by 3 is
\(\frac{9}{{87}}\)
\(\frac{{12}}{{87}}\)
\(\frac{{15}}{{87}}\)
\(\frac{{47}}{{87}}\)
Question:Two friends A and B have equal number of daughters. There are three cinema tickets which are to be distributed among the daughters of A and B. The probability that all the tickets go to daughters of A is 1/20. The number of daughters each of them have is
4
5
6
3
Question:If a committee of 3 is to be chosen from a group of 38 people of which you are a member. What is the probability that you will be on the committee
\(\left( \begin{array}{l} 38 \\ \,3 \\ \end{array} \right)\)
\(\left( \begin{array}{l} 37 \\ \,2 \\ \end{array} \right)\)
\({{\left( \begin{array}{l} 37 \\ \,2 \\ \end{array} \right)} \mathord{\left/ {\vphantom {{\left( \begin{array}{l} 37 \\ \,2 \\ \end{array} \right)} {\left( \begin{array}{l} 38 \\ \,3 \\ \end{array} \right)}}}
\right. \kern-\nulldelimiterspace} {\left( \begin{array}{l} 38 \\ \,3 \\ \end{array} \right)}}\) \(\frac{{666}}{{8436}}\)
Question:Four boys and three girls stand in a queue for an interview, probability that they will in alternate position is
\(\frac{1}{{34}}\)
\(\frac{1}{{35}}\)
\(\frac{1}{{17}}\)
\(\frac{1}{{68}}\)
Question:A drawer contains 5 brown socks and 4 blue socks well mixed. A man reaches the drawer and pulls out 2 socks at random. What is the probability that they match
\(\frac{4}{9}\)
\(\frac{5}{8}\)
\(\frac{5}{9}\)
Question:5 persons A, B, C, D and E are in queue of a shop. The probability that A and E always together, is
Question:If odds against solving a question by three students are 2 : 1, \(5:2\) and \(5:3\) respectively, then probability that the question is solved only by one student is
\(\frac{{31}}{{56}}\)
\(\frac{{24}}{{56}}\)
\(\frac{{25}}{{56}}\)
Question:Three ships A, B and C sail from England to India. If the ratio of their arriving safely are 2 : 5, 3 : 7 and 6 : 11 respectively then the probability of all the ships for arriving safely is
\(\frac{{18}}{{595}}\)
\(\frac{6}{{17}}\)
\(\frac{3}{{10}}\)
Question:The chances to fail in Physics are 20% and the chances to fail in Mathematics are 10%. What are the chances to fail in at least one subject
28%
38%
72%
82%
Question:If \(P\,(A) = \frac{1}{4},\,\,P\,(B) = \frac{5}{8}\) and \(P\,(A \cup B) = \frac{3}{4},\) then \(P\,(A \cap B) = \)
Question:Three athlete A, B and C participate in a race competetion. The probability of winning A and B is twice of winning C. Then the probability that the race win by A or B, is
Question:If \(P(A) = \frac{1}{2},\,\,P(B) = \frac{1}{3}\) and \(P(A \cap B) = \frac{7}{{12}},\) then the value of \(P\,(A' \cap B')\) is
\(\frac{1}{6}\)
Question:One card is drawn randomly from a pack of 52 cards, then the probability that it is a king or spade is
\(\frac{3}{{26}}\)
\(\frac{4}{{13}}\)
\(\frac{3}{{13}}\)
Question:If \(P(A) = 0.25,\,\,P(B) = 0.50\) and \(P(A \cap B) = 0.14,\) then \(P(A \cap \bar B)\) is equal to
0.61
0.39
0.48
Question:If A and B are two events such that \(P\,(A) \ne 0\) and \(P\,(B) \ne 1,\) then \(P\,\left( {\frac{{\bar A}}{{\bar B}}} \right) = \)
\(1 - P\,\left( {\frac{A}{B}} \right)\)
\(1 - P\,\left( {\frac{{\bar A}}{B}} \right)\)
\(\frac{{1 - P\,(A \cup B)}}{{P\,(\bar B)}}\)
\(\frac{{P\,(\bar A)}}{{P\,(\bar B)}}\)
Question:In a single throw of two dice what is the probability of obtaining a number greater than 7, if 4 appears on the first dice
Question:In a certain town, 40% of the people have brown hair, 25% have brown eyes and 15% have both brown hair and brown eyes. If a person selected at random from the town, has brown hair, the probability that he also has brown eyes, is
\(\frac{3}{8}\)
Question:There are 3 bags which are known to contain 2 white and 3 black balls; 4 white and 1 black balls and 3 white and 7 black balls respectively. A ball is drawn at random from one of the bags and found to be a black ball. Then the probability that it was drawn from the bag containing the most black balls is
\(\frac{7}{{15}}\)
\(\frac{5}{{19}}\)
Question:If the probability that a student is not a swimmer is 1/5, then the probability that out of 5 students one is swimmer is
\(^5{C_1}{\left( {\frac{4}{5}} \right)^4}\left( {\frac{1}{5}} \right)\)
\(^5{C_1}\,\frac{4}{5}\,{\left( {\frac{1}{5}} \right)^4}\)
\(\frac{4}{5}{\left( {\frac{1}{5}} \right)^4}\)
Question:In a box of 10 electric bulbs, two are defective. Two bulbs are selected at random one after the other from the box. The first bulb after selection being put back in the box before making the second selection. The probability that both the bulbs are without defect is
\(\frac{9}{{25}}\)
\(\frac{{16}}{{25}}\)
\(\frac{8}{{25}}\)
Question:A die is tossed twice. Getting a number greater than 4 is considered a success. Then the variance of the probability distribution of the number of successes is
\(\frac{2}{9}\)
Question:A die is thrown three times. Getting a 3 or a 6 is considered success. Then the probability of at least two successes is
\(\frac{7}{{27}}\)
\(\frac{1}{{27}}\)
Question:The records of a hospital show that 10% of the cases of a certain disease are fatal. If 6 patients are suffering from the disease, then the probability that only three will die is
\(1458 \times {10^{ - 5}}\)
\(1458 \times {10^{ - 6}}\)
\(41 \times {10^{ - 6}}\)
\(8748 \times {10^{ - 5}}\)
Question:Assuming that for a husband-wife couple the chances of their child being a boy or a girl are the same, the probability of their two children being a boy and a girl is
Question:A coin is tossed 3 times. The probability of getting exactly two heads is
Question:One coin is thrown 100 times. The probability of coming tail in odd number