Probability Test 6

Total Questions:50 Total Time: 75 Min

Remaining:

 

Questions 1 of 50

Question:A single letter is selected at random from the word "PROBABILITY". The probability that the selected letter is a vowel is

Answers Choices:

\(\frac{2}{{11}}\)

\(\frac{3}{{11}}\)

\(\frac{4}{{11}}\)

0

Questions 2 of 50

Question:There are n letters and n addressed envelopes. The probability that all the letters are not kept in the right envelope, is

Answers Choices:

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

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

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

None of these

Questions 3 of 50

Question:Two dice are thrown. The probability that the sum of numbers appearing is more than 10, is

Answers Choices:

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

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

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

None of these

Questions 4 of 50

Question:The probability of getting a total of 5 or 6 in a single throw of 2 dice is

Answers Choices:

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

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

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

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

Questions 5 of 50

Question:If in a lottary there are 5 prizes and 20 blanks, then the probability of getting a prize is

Answers Choices:

\(\frac{1}{5}\)

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

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

None of these

Questions 6 of 50

Question:The probability of getting a number greater than 2 in throwing a die is

Answers Choices:

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

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

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

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

Questions 7 of 50

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

Answers Choices:

0.00000625

0.18543125

0.00001875

0.81450625

Questions 8 of 50

Question:The chance of throwing at least 9 in a single throw with two dice, is

Answers Choices:

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

\(\frac{5}{{18}}\)

\(\frac{7}{{18}}\)

\(\frac{{11}}{{18}}\)

Questions 9 of 50

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

Answers Choices:

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

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

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

None of these

Questions 10 of 50

Question:The event A is independent of itself if and only if \(P(A) = \)

Answers Choices:

0

1

0, 1

None of these

Questions 11 of 50

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

Answers Choices:

\(\frac{8}{{25}}\)

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

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

\(\frac{{21}}{{25}}\)

Questions 12 of 50

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

Answers Choices:

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

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

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

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

Questions 13 of 50

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

Answers Choices:

\(\frac{1}{5}\)

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

\(\frac{3}{{40}}\)

\(\frac{{29}}{{40}}\)

Questions 14 of 50

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

Answers Choices:

\(\frac{1}{{13}}\)

\(\frac{2}{{13}}\)

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

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

Questions 15 of 50

Question:The probability that in a year of the 22nd century chosen at random there will be 53 Sundays is

Answers Choices:

\(\frac{3}{{28}}\)

\(\frac{2}{{28}}\)

\(\frac{7}{{28}}\)

\(\frac{5}{{28}}\)

Questions 16 of 50

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

Answers Choices:

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

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

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

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

Questions 17 of 50

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

Answers Choices:

\(\frac{{99}}{{323}}\)

\(\frac{{224}}{{323}}\)

\(\frac{{100}}{{323}}\)

None of these

Questions 18 of 50

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

Answers Choices:

\(\frac{1}{{10}}\)

\(\frac{1}{{15}}\)

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

\(\frac{2}{{21}}\)

Questions 19 of 50

Question:In a throw of a dice the probability of getting one in even number of throw is

Answers Choices:

\(\frac{5}{{36}}\)

\(\frac{5}{{11}}\)

\(\frac{6}{{11}}\)

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

Questions 20 of 50

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

Answers Choices:

2/3

1/6

5/6

1/3

Questions 21 of 50

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

Answers Choices:

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

\(\frac{5}{9}\)

\(\frac{4}{9}\)

\(\frac{2}{9}\)

Questions 22 of 50

Question:The letter of the word `ASSASSIN' are written down at random in a row. The probability that no two S occur together is

Answers Choices:

\(\frac{1}{{35}}\)

\(\frac{1}{{14}}\)

\(\frac{1}{{15}}\)

None of these

Questions 23 of 50

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

Answers Choices:

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

\(\frac{1}{5}\)

\(\frac{1}{{10}}\)

\(\frac{1}{{20}}\)

Questions 24 of 50

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

Answers Choices:

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

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

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

None of these

Questions 25 of 50

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

Answers Choices:

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

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

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

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

Questions 26 of 50

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

Answers Choices:

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

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

\(\frac{1}{{60}}\)

\(\frac{1}{{56}}\)

Questions 27 of 50

Question:Three integers are chosen at random from the first 20 integers. The probability that their product is even, is

Answers Choices:

\(\frac{2}{{19}}\)

\(\frac{3}{{29}}\)

\(\frac{{17}}{{19}}\)

\(\frac{4}{{19}}\)

Questions 28 of 50

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

Answers Choices:

\(\frac{1}{{15}}\)

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

\(\frac{1}{5}\)

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

Questions 29 of 50

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

Answers Choices:

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

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

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

None of these

Questions 30 of 50

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

Answers Choices:

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

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

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

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

Questions 31 of 50

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

Answers Choices:

0.125

0.25

0.375

0.5

Questions 32 of 50

Question:A card is drawn at random from a pack of cards. The probability of this card being a red or a queen is

Answers Choices:

\(\frac{1}{{13}}\)

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

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

\(\frac{7}{{13}}\)

Questions 33 of 50

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 \(P\,(A) = \)

Answers Choices:

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

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

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

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

Questions 34 of 50

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 \(P\,(A) = \)

Answers Choices:

\(\frac{7}{{12}}\)

\(\frac{7}{{24}}\)

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

\(\frac{{17}}{{24}}\)

Questions 35 of 50

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

Answers Choices:

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

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

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

\(P(A)\,\,.\,\,P(B)\)

Questions 36 of 50

Question:If \({A_1},\,{A_2},...{A_n}\) are any n events, then

Answers Choices:

\(P\,({A_1} \cup {A_2} \cup ... \cup {A_n}) = P\,({A_1}) + P({A_2}) + ... + P\,({A_n})\)

\(P\,({A_1} \cup {A_2} \cup ... \cup {A_n}) > P\,({A_1}) + P({A_2}) + ... + P\,({A_n})\)

\(P\,({A_1} \cup {A_2} \cup ... \cup {A_n}) \le P\,({A_1}) + P({A_2}) + ... + P\,({A_n})\)

None of these

Questions 37 of 50

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

Answers Choices:

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

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

\(\frac{5}{8}\)

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

Questions 38 of 50

Question:If \(P(A) = P(B) = x\) and \(P(A \cap B) = P(A' \cap B') = \frac{1}{3}\), then \(x = \)

Answers Choices:

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

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

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

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

Questions 39 of 50

Question:If A and B are two independent events, then \(P\,\left( {\frac{A}{B}} \right) = \)

Answers Choices:

0

1

\(P\,(A)\)

\(P\,(B)\)

Questions 40 of 50

Question:If E and F are independent events such that \(0 < P(E) < 1\) and \(0 < P\,(F) < 1,\) then

Answers Choices:

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

Questions 41 of 50

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

Answers Choices:

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

Questions 42 of 50

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)

Answers Choices:

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

\(\frac{5}{{52}}\)

\(\frac{5}{{221}}\)

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

Questions 43 of 50

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

Answers Choices:

\(\frac{{144}}{{625}}\)

\(\frac{{72}}{{3125}}\)

\(\frac{{216}}{{625}}\)

None of these

Questions 44 of 50

Question:If a dice is thrown 5 times, then the probability of getting 6 exact three times, is

Answers Choices:

\(\frac{{125}}{{388}}\)

\(\frac{{125}}{{3888}}\)

\(\frac{{625}}{{23328}}\)

\(\frac{{250}}{{2332}}\)

Questions 45 of 50

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

Answers Choices:

\(\frac{{35}}{{{2^{12}}}}\)

\(\frac{{35}}{{{2^{14}}}}\)

\(\frac{7}{{{2^{12}}}}\)

None of these

Questions 46 of 50

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

Answers Choices:

\(\frac{8}{{{3^7}}}\)

\(\frac{{16}}{{{3^7}}}\)

\(\frac{{280}}{{{3^7}}}\)

\(\frac{{560}}{{{3^7}}}\)

Questions 47 of 50

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

Answers Choices:

\(\frac{8}{{141}}\)

\(\frac{{10}}{{243}}\)

\(\frac{{11}}{{243}}\)

\(\frac{8}{{41}}\)

Questions 48 of 50

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

Answers Choices:

\(\frac{{(2n!)}}{{{{(n!)}^2}}}{\left( {\frac{1}{2}} \right)^{2n}}\)

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

\(1 - \frac{{(2n!)}}{{{{(n!)}^2}}}\,.\,\frac{1}{{{4^n}}}\)

None of these

Questions 49 of 50

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

Answers Choices:

1/13

3/13

2/13

None of these

Questions 50 of 50

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

Answers Choices:

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

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

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

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