Probability Test 3

Total Questions:50 Total Time: 75 Min

Remaining:

 

Questions 1 of 50

Question:Two card are drawn successively with replacement from a pack of 52 cards. The probability of drawing two aces is

Answers Choices:

\(\frac{1}{{169}}\)

\(\frac{1}{{221}}\)

\(\frac{1}{{2652}}\)

\(\frac{4}{{663}}\)

Questions 2 of 50

Question:In a single throw of two dice, the probability of getting more than 7 is

Answers Choices:

\(\frac{7}{{36}}\)

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

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

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

Questions 3 of 50

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

Answers Choices:

1

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

\(\frac{7}{{36}}\)

None of these

Questions 4 of 50

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

Answers Choices:

\(\frac{{33}}{{221}}\)

\(\frac{{188}}{{221}}\)

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

\(\frac{{21}}{{221}}\)

Questions 5 of 50

Question:In a simultaneous throw of three coins, what is the probability of getting at least 2 tails

Answers Choices:

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

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

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

None of these

Questions 6 of 50

Question:In a throw of a die, what is the probability of getting a number less than 7

Answers Choices:

0

1

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

None of these

Questions 7 of 50

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

Answers Choices:

\(\frac{{24}}{{64}}\)

\(\frac{{40}}{{64}}\)

\(\frac{{49}}{{64}}\)

\(\frac{{64}}{{64}}\)

Questions 8 of 50

Question:The probability of happening of an impossible event i.e. \(P\,(\varphi )\) is

Answers Choices:

1

0

2

1

Questions 9 of 50

Question:A number is chosen from first 100 natural numbers. The probability that the number is even or divisible by 5, is

Answers Choices:

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

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

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

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

Questions 10 of 50

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

Answers Choices:

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

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

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

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

Questions 11 of 50

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

Answers Choices:

\(\frac{{11}}{{24}}\)

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

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

None of these

Questions 12 of 50

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

Answers Choices:

3/16

3/8

1/4

None of these

Questions 13 of 50

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

Answers Choices:

\(\frac{1}{{1260}}\)

\(\frac{1}{{7560}}\)

\(\frac{1}{{126}}\)

None of these

Questions 14 of 50

Question:A dice is rolled three times, the probability of getting a larger number than the previous number each time is

Answers Choices:

\(\frac{{15}}{{216}}\)

\(\frac{5}{{54}}\)

\(\frac{{13}}{{216}}\)

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

Questions 15 of 50

Question:The sum of two positive numbers is 100. The probability that their product is greater than 1000 is

Answers Choices:

\(\frac{7}{9}\)

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

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

None of these

Questions 16 of 50

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

Answers Choices:

\(\frac{5}{{24}}\)

\(\frac{5}{{64}}\)

\(\frac{3}{{32}}\)

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

Questions 17 of 50

Question:The probability that a leap year will have 53 Fridays or 53 Saturdays is

Answers Choices:

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

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

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

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

Questions 18 of 50

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)

Answers Choices:

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

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

\(\frac{1}{{40}}\)

None of these

Questions 19 of 50

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

Answers Choices:

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

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

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

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

Questions 20 of 50

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

Answers Choices:

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

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

\(\frac{7}{{20}}\)

\(\frac{3}{{20}}\)

Questions 21 of 50

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

Answers Choices:

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

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

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

None of these

Questions 22 of 50

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

Answers Choices:

\(\frac{3}{{190}}\)

\(\frac{1}{{19}}\)

\(\frac{1}{{190}}\)

None of these

Questions 23 of 50

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

Answers Choices:

\(\frac{5}{{1296}}\)

\(\frac{5}{{1944}}\)

\(\frac{5}{{2592}}\)

None of these

Questions 24 of 50

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

Answers Choices:

\({p_1} = {p_2}\)

\({p_1} < {p_2}\)

\({p_1} > {p_2}\)

None of these

Questions 25 of 50

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

Answers Choices:

\(\frac{9}{{87}}\)

\(\frac{{12}}{{87}}\)

\(\frac{{15}}{{87}}\)

\(\frac{{47}}{{87}}\)

Questions 26 of 50

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

Answers Choices:

4

5

6

3

Questions 27 of 50

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

Answers Choices:

\(\left( \begin{array}{l} 38 \\ \,3 \\ \end{array} \right)\)

\(\left( \begin{array}{l} 37 \\ \,2 \\ \end{array} \right)\)

\({{\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)}}\) \(\frac{{666}}{{8436}}\)

Questions 28 of 50

Question:Four boys and three girls stand in a queue for an interview, probability that they will in alternate position is

Answers Choices:

\(\frac{1}{{34}}\)

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

\(\frac{1}{{17}}\)

\(\frac{1}{{68}}\)

Questions 29 of 50

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

Answers Choices:

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

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

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

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

Questions 30 of 50

Question:5 persons A, B, C, D and E are in queue of a shop. The probability that A and E always together, is

Answers Choices:

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

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

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

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

Questions 31 of 50

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

Answers Choices:

\(\frac{{31}}{{56}}\)

\(\frac{{24}}{{56}}\)

\(\frac{{25}}{{56}}\)

None of these

Questions 32 of 50

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

Answers Choices:

\(\frac{{18}}{{595}}\)

\(\frac{6}{{17}}\)

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

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

Questions 33 of 50

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

Answers Choices:

28%

38%

72%

82%

Questions 34 of 50

Question:If \(P\,(A) = \frac{1}{4},\,\,P\,(B) = \frac{5}{8}\) and \(P\,(A \cup B) = \frac{3}{4},\) then \(P\,(A \cap B) = \)

Answers Choices:

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

0

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

1

Questions 35 of 50

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

Answers Choices:

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

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

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

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

Questions 36 of 50

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

Answers Choices:

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

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

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

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

Questions 37 of 50

Question:One card is drawn randomly from a pack of 52 cards, then the probability that it is a king or spade is

Answers Choices:

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

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

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

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

Questions 38 of 50

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

Answers Choices:

0.61

0.39

0.48

None of these

Questions 39 of 50

Question:If A and B are two events such that \(P\,(A) \ne 0\) and \(P\,(B) \ne 1,\) then \(P\,\left( {\frac{{\bar A}}{{\bar B}}} \right) = \)

Answers Choices:

\(1 - P\,\left( {\frac{A}{B}} \right)\)

\(1 - P\,\left( {\frac{{\bar A}}{B}} \right)\)

\(\frac{{1 - P\,(A \cup B)}}{{P\,(\bar B)}}\)

\(\frac{{P\,(\bar A)}}{{P\,(\bar B)}}\)

Questions 40 of 50

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

Answers Choices:

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

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

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

None of these

Questions 41 of 50

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

Answers Choices:

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

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

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

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

Questions 42 of 50

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

Answers Choices:

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

\(\frac{5}{{19}}\)

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

None of these

Questions 43 of 50

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

Answers Choices:

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

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

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

None of these

Questions 44 of 50

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

Answers Choices:

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

\(\frac{{16}}{{25}}\)

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

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

Questions 45 of 50

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

Answers Choices:

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

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

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

None of these

Questions 46 of 50

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

Answers Choices:

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

\(\frac{7}{{27}}\)

\(\frac{1}{{27}}\)

None of these

Questions 47 of 50

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

Answers Choices:

\(1458 \times {10^{ - 5}}\)

\(1458 \times {10^{ - 6}}\)

\(41 \times {10^{ - 6}}\)

\(8748 \times {10^{ - 5}}\)

Questions 48 of 50

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

Answers Choices:

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

1

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

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

Questions 49 of 50

Question:A coin is tossed 3 times. The probability of getting exactly two heads is

Answers Choices:

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

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

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

None of these

Questions 50 of 50

Question:One coin is thrown 100 times. The probability of coming tail in odd number

Answers Choices:

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

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

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

None of these