Total Questions:50 Total Time: 75 Min
Remaining:
Question:A single letter is selected at random from the word "PROBABILITY". The probability that the selected letter is a vowel is
\(\frac{2}{{11}}\)
\(\frac{3}{{11}}\)
\(\frac{4}{{11}}\)
0
Question:There are n letters and n addressed envelopes. The probability that all the letters are not kept in the right envelope, is
\(\frac{1}{{n\,!}}\)
\(1 - \frac{1}{{n\,!}}\)
\(1 - \frac{1}{n}\)
None of these
Question:Two dice are thrown. The probability that the sum of numbers appearing is more than 10, is
\(\frac{1}{{18}}\)
\(\frac{1}{{12}}\)
\(\frac{1}{6}\)
Question:The probability of getting a total of 5 or 6 in a single throw of 2 dice is
\(\frac{1}{2}\)
\(\frac{1}{4}\)
\(\frac{1}{3}\)
Question:If in a lottary there are 5 prizes and 20 blanks, then the probability of getting a prize is
\(\frac{1}{5}\)
\(\frac{2}{5}\)
\(\frac{4}{5}\)
Question:The probability of getting a number greater than 2 in throwing a die is
\(\frac{2}{3}\)
Question:The probability that an event will fail to happen is 0.05. The probability that the event will take place on 4 consecutive occasions is
0.00000625
0.18543125
0.00001875
0.81450625
Question:The chance of throwing at least 9 in a single throw with two dice, is
\(\frac{5}{{18}}\)
\(\frac{7}{{18}}\)
\(\frac{{11}}{{18}}\)
Question:A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant chosen is non-zero is
\(\frac{3}{{16}}\)
\(\frac{3}{8}\)
Question:The event A is independent of itself if and only if \(P(A) = \)
1
0, 1
Question:A box contains 3 white and 2 red balls. A ball is drawn and another ball is drawn without replacing first ball, then the probability of second ball to be red is
\(\frac{8}{{25}}\)
\(\frac{3}{5}\)
\(\frac{{21}}{{25}}\)
Question:The probability of India winning a test match against West Indies is \(\frac{1}{2}\). Assuming independence from match to match, the probability that in a 5 match series India's second win occurs at the third test, is
\(\frac{1}{8}\)
Question:The chance of India winning toss is 3/4. If it wins the toss, then its chance of victory is 4/5 otherwise it is only 1/2. Then chance of India's victory is
\(\frac{3}{{40}}\)
\(\frac{{29}}{{40}}\)
Question:From a pack of 52 cards one card is drawn at random, the probability that it is either a king or a queen is
\(\frac{1}{{13}}\)
\(\frac{2}{{13}}\)
\(\frac{3}{{13}}\)
\(\frac{4}{{13}}\)
Question:The probability that in a year of the 22nd century chosen at random there will be 53 Sundays is
\(\frac{3}{{28}}\)
\(\frac{2}{{28}}\)
\(\frac{7}{{28}}\)
\(\frac{5}{{28}}\)
Question:Suppose that a die (with faces marked 1 to 6) is loaded in such a manner that for K = 1, 2, 3..........., 6, the probability of the face marked K turning up when die is tossed is proportional to K. The probability of the event that the outcome of a toss of the die will be an even number is equal to
\(\frac{4}{7}\)
\(\frac{1}{{21}}\)
Question:There are 10 pairs of shoes in a cupboard from which 4 shoes are picked at random. The probability that there is at least one pair, is
\(\frac{{99}}{{323}}\)
\(\frac{{224}}{{323}}\)
\(\frac{{100}}{{323}}\)
Question:A bag contains 3 red and 7 black balls, two balls are taken out at random, without replacement. If the first ball taken out is red, then what is the probability that the second taken out ball is also red
\(\frac{1}{{10}}\)
\(\frac{1}{{15}}\)
\(\frac{3}{{10}}\)
\(\frac{2}{{21}}\)
Question:In a throw of a dice the probability of getting one in even number of throw is
\(\frac{5}{{36}}\)
\(\frac{5}{{11}}\)
\(\frac{6}{{11}}\)
Question:A and B are two independent events such that \(P(A) = 1/2\)and \(P(B) = 1/3\). Then P (neither A nor B) is equal to
2/3
1/6
5/6
1/3
Question:A committee of five is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all, is
\(\frac{5}{9}\)
\(\frac{4}{9}\)
\(\frac{2}{9}\)
Question:The letter of the word `ASSASSIN' are written down at random in a row. The probability that no two S occur together is
\(\frac{1}{{35}}\)
\(\frac{1}{{14}}\)
Question:Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices is equilateral, is equal to
\(\frac{1}{{20}}\)
Question:Three mangoes and three apples are in a box. If two fruits are chosen at random, the probability that one is a mango and the other is an apple is
Question:A bag contains 4 white and 3 red balls. Two draws of one ball each are made without replacement. Then the probability that both the balls are red is
\(\frac{1}{7}\)
\(\frac{2}{7}\)
\(\frac{3}{7}\)
Question:A bag contains 5 white, 7 black and 4 red balls. Three balls are drawn from the bag at random. The probability that all the three balls are white, is
\(\frac{1}{{60}}\)
\(\frac{1}{{56}}\)
Question:Three integers are chosen at random from the first 20 integers. The probability that their product is even, is
\(\frac{2}{{19}}\)
\(\frac{3}{{29}}\)
\(\frac{{17}}{{19}}\)
\(\frac{4}{{19}}\)
Question:Two numbers are selected randomly from the set \(S = \{ 1,\,2,\,3,\,4,\,5,\,6\} \) without replacement one by one. The probability that minimum of the two numbers is less than 4 is
\(\frac{{14}}{{15}}\)
Question:Suppose \(n \ge 3\) persons are sitting in a row. Two of them are selected at random. The probability that they are not together is
\(1 - \frac{2}{n}\)
\(\frac{2}{{n - 1}}\)
Question:Fifteen persons among whom are A and B, sit down at random at a round table. The probability that there are 4 persons between A and B, is
Question:Suppose that A, B, C are events such that \(P\,(A) = P\,(B) = P\,(C) = \frac{1}{4},\,P\,(AB) = P\,(CB) = 0,\,P\,(AC) = \frac{1}{8},\) then \(P\,(A + B) = \)
0.125
0.25
0.375
0.5
Question:A card is drawn at random from a pack of cards. The probability of this card being a red or a queen is
\(\frac{1}{{26}}\)
\(\frac{7}{{13}}\)
Question:If A and B an two events such that \(P\,(A \cup B) = \frac{5}{6}\),\(P\,(A \cap B) = \frac{1}{3}\) and \(P\,(\bar B) = \frac{1}{3},\) then \(P\,(A) = \)
Question:If A and B are two events such that \(P\,(A \cup B)\, + P\,(A \cap B) = \frac{7}{8}\) and \(P\,(A) = 2\,P\,(B),\) then \(P\,(A) = \)
\(\frac{7}{{12}}\)
\(\frac{7}{{24}}\)
\(\frac{5}{{12}}\)
\(\frac{{17}}{{24}}\)
Question:If A and B are any two events, then \(P(A \cup B) = \)
\(P(A) + P(B)\)
\(P(A) + P(B) + P(A \cap B)\)
\(P(A) + P(B) - P(A \cap B)\)
\(P(A)\,\,.\,\,P(B)\)
Question:If \({A_1},\,{A_2},...{A_n}\) are any n events, then
\(P\,({A_1} \cup {A_2} \cup ... \cup {A_n}) = P\,({A_1}) + P({A_2}) + ... + P\,({A_n})\)
\(P\,({A_1} \cup {A_2} \cup ... \cup {A_n}) > P\,({A_1}) + P({A_2}) + ... + P\,({A_n})\)
\(P\,({A_1} \cup {A_2} \cup ... \cup {A_n}) \le P\,({A_1}) + P({A_2}) + ... + P\,({A_n})\)
Question:If A and B are events such that \(P(A \cup B) = 3/4,\) \(P(A \cap B) = 1/4,\) \(P(\bar A) = 2/3,\) then \(P(\bar A \cap B)\) is
\(\frac{5}{8}\)
Question:If \(P(A) = P(B) = x\) and \(P(A \cap B) = P(A' \cap B') = \frac{1}{3}\), then \(x = \)
Question:If A and B are two independent events, then \(P\,\left( {\frac{A}{B}} \right) = \)
\(P\,(A)\)
\(P\,(B)\)
Question:If E and F are independent events such that \(0 < P(E) < 1\) and \(0 < P\,(F) < 1,\) then
E and \({F^c}\)(the complement of the event F) are independent
\({E^c}\)and \({F^c}\)are independent
\(P\,\left( {\frac{E}{F}} \right) + P\,\left( {\frac{{{E^c}}}{{{F^c}}}} \right) = 1\)
All of the above
Question:For two events A and B, if \(P(A) = P\left( {\frac{A}{B}} \right) = \frac{1}{4}\) and \(P\left( {\frac{B}{A}} \right) = \frac{1}{2}\), then
A and B are independent
\(P\left( {\frac{{A'}}{B}} \right) = \frac{3}{4}\)
\(P\left( {\frac{{B'}}{{A'}}} \right) = \frac{1}{2}\)
All of these
Question:Two cards are drawn one by one from a pack of cards. The probability of getting first card an ace and second a coloured one is (before drawing second card first card is not placed again in the pack)
\(\frac{5}{{52}}\)
\(\frac{5}{{221}}\)
Question:A man make attempts to hit the target. The probability of hitting the target is \(\frac{3}{5}.\) Then the probability that A hit the target exactly 2 times in 5 attempts, is
\(\frac{{144}}{{625}}\)
\(\frac{{72}}{{3125}}\)
\(\frac{{216}}{{625}}\)
Question:If a dice is thrown 5 times, then the probability of getting 6 exact three times, is
\(\frac{{125}}{{388}}\)
\(\frac{{125}}{{3888}}\)
\(\frac{{625}}{{23328}}\)
\(\frac{{250}}{{2332}}\)
Question:A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to that of getting 9 heads, then the probability of getting 3 heads is
\(\frac{{35}}{{{2^{12}}}}\)
\(\frac{{35}}{{{2^{14}}}}\)
\(\frac{7}{{{2^{12}}}}\)
Question:A contest consists of predicting the results win, draw or defeat of 7 football matches. A sent his entry by predicting at random. The probability that his entry will contain exactly 4 correct predictions is
\(\frac{8}{{{3^7}}}\)
\(\frac{{16}}{{{3^7}}}\)
\(\frac{{280}}{{{3^7}}}\)
\(\frac{{560}}{{{3^7}}}\)
Question:A bag contains 2 white and 4 black balls. A ball is drawn 5 times with replacement. The probability that at least 4 of the balls drawn are white is
\(\frac{8}{{141}}\)
\(\frac{{10}}{{243}}\)
\(\frac{{11}}{{243}}\)
\(\frac{8}{{41}}\)
Question:A coin is tossed 2n times. The chance that the number of times one gets head is not equal to the number of times one gets tail is
\(\frac{{(2n!)}}{{{{(n!)}^2}}}{\left( {\frac{1}{2}} \right)^{2n}}\)
\(1 - \frac{{(2n!)}}{{{{(n!)}^2}}}\)
\(1 - \frac{{(2n!)}}{{{{(n!)}^2}}}\,.\,\frac{1}{{{4^n}}}\)
Question:Two cards are drawn successively with replacement from a well shuffled deck of 52 cards then the mean of the number of aces is
1/13
3/13
2/13
Question:A sample of 4 items is drawn at a random without replacement from a lot of 10 items. Containing 3 defective. If X denotes the number of defective items in the sample then \(P(0 < x < 3)\) is equal to