Probability Test 2

Total Questions:50 Total Time: 75 Min

Remaining:

 

Questions 1 of 50

Question:Let A, B, C be three mutually independent events. Consider the two statements \({S_1}\)and \({S_2}\)\({S_1}\,\,:\,\,A\) and \(B \cup C\) are independent\({S_2}\,\,:\,\,A\) and \(B \cap C\) are independentThen

Answers Choices:

Both \({S_1}\) and \({S_2}\) are true

Only \({S_1}\) is true

Only \({S_2}\) is true

Neither \({S_1}\) nor \({S_2}\) is true

Questions 2 of 50

Question:If \(P(A) = 2/3\), \(P(B) = 1/2\) and \({\rm{ }}P(A \cup B) = 5/6\) then events A and B are

Answers Choices:

Mutually exclusive

Independent as well as mutually exhaustive

Independent

Dependent only on A

Questions 3 of 50

Question:From a pack of 52 cards two are drawn with replacement. The probability, that the first is a diamond and the second is a king, is

Answers Choices:

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

\(\frac{{17}}{{2704}}\)

\(\frac{1}{{52}}\)

None of these

Questions 4 of 50

Question:Two dice are thrown simultaneously. The probability of getting the sum 2 or 8 or 12 is

Answers Choices:

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

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

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

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

Questions 5 of 50

Question:The probability of getting number 5 in throwing a dice is

Answers Choices:

1

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

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

\(\frac{5}{6}\)

Questions 6 of 50

Question:A card is drawn from a well shuffled pack of cards. The probability of getting a queen of club or king of heart is

Answers Choices:

\(\frac{1}{{52}}\)

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

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

None of these

Questions 7 of 50

Question:In a single throw of two dice what is the probability of getting a total 13

Answers Choices:

0

1

\(\frac{{13}}{{36}}\)

\(\frac{{25}}{{36}}\)

Questions 8 of 50

Question:Three dice are thrown simultaneously. What is the probability of obtaining a total of 17 or 18

Answers Choices:

\(\frac{1}{9}\)

\(\frac{1}{{72}}\)

\(\frac{1}{{54}}\)

None of these

Questions 9 of 50

Question:If A is a sure event, then the value of P (A not ) is

Answers Choices:

0

1

1

None of these

Questions 10 of 50

Question:A number is chosen at random from first ten natural numbers. The probability that number is odd and perfect square is

Answers Choices:

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

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

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

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

Questions 11 of 50

Question:In a single throw of two dice, the probability of obtaining a total of 7 or 9, is

Answers Choices:

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

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

\(\frac{1}{9}\)

None of these

Questions 12 of 50

Question:A bag contains 19 tickets numbered from 1 to 19. A ticket is drawn and then another ticket is drawn without replacement. The probability that both the tickets will show even number, is

Answers Choices:

\(\frac{9}{{19}}\)

\(\frac{8}{{18}}\)

\(\frac{9}{{18}}\)

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

Questions 13 of 50

Question:A bag contains 3 black and 4 white balls. Two balls are drawn one by one at random without replacement. The probability that the second drawn ball is white, is

Answers Choices:

\(\frac{4}{{49}}\)

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

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

\(\frac{{12}}{{49}}\)

Questions 14 of 50

Question:'A' draws two cards with replacement from a pack of 52 cards and 'B' throws a pair of dice what is the chance that 'A' gets both cards of same suit and 'B' gets total of 6

Answers Choices:

\(\frac{1}{{144}}\)

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

\(\frac{5}{{144}}\)

\(\frac{7}{{144}}\)

Questions 15 of 50

Question:A fair coin is tossed repeatedly. If tail appears on first four tosses then the probability of head appearing on fifth toss equals

Answers Choices:

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

\(\frac{1}{{32}}\)

\(\frac{{31}}{{32}}\)

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

Questions 16 of 50

Question:A coin is tossed 3 times by 2 persons. What is the probability that both get equal number of heads

Answers Choices:

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

\(\frac{1}{9}\)

\(\frac{5}{{16}}\)

None of these

Questions 17 of 50

Question:If any four numbers are selected and they are multiplied, then the probability that the last digit will be 1, 3, 5 or 7 is

Answers Choices:

\(\frac{4}{{625}}\)

\(\frac{{18}}{{625}}\)

\(\frac{{16}}{{625}}\)

None of these

Questions 18 of 50

Question:If a coin be tossed n times then probability that the head comes odd times is

Answers Choices:

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

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

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

None of these

Questions 19 of 50

Question:Four coins are tossed. The probability that at least one head turns up, is

Answers Choices:

1/16

1/4

15/16

None of these

Questions 20 of 50

Question:Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is

Answers Choices:

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

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

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

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

Questions 21 of 50

Question:A box contains 25 tickets numbered 1, 2, ....... 25. If two tickets are drawn at random then the probability that the product of their numbers is even, is

Answers Choices:

\(\frac{{11}}{{50}}\)

\(\frac{{13}}{{50}}\)

\(\frac{{37}}{{50}}\)

None of these

Questions 22 of 50

Question:From a class of 12 girls and 18 boys, two students are chosen randomly. What is the probability that both of them are girls

Answers Choices:

\(\frac{{22}}{{145}}\)

\(\frac{{13}}{{15}}\)

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

None of these

Questions 23 of 50

Question:Word "UNIVERSITY" is arranged randomly. Then the probability that both "I" does not come together, is

Answers Choices:

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

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

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

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

Questions 24 of 50

Question:There are n different objects 1, 2, 3,......n distributed at random in n places marked 1, 2, 3, ......n. The probability that at least three of the objects occupy places corresponding to their number is

Answers Choices:

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

\(\frac{5}{6}\)

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

None of these

Questions 25 of 50

Question:A box contains 10 mangoes out of which 4 are rotten. 2 mangoes are taken out together. If one of them is found to be good, the probability that the other is also good is

Answers Choices:

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

\(\frac{8}{{15}}\)

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

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

Questions 26 of 50

Question:Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of the selected persons will be a woman is

Answers Choices:

\(\frac{{25}}{{39}}\)

\(\frac{{14}}{{39}}\)

\(\frac{5}{{13}}\)

\(\frac{{10}}{{13}}\)

Questions 27 of 50

Question:If four vertices of a regular octagon are chosen at random, then the probability that the quadrilateral formed by them is a rectangle is

Answers Choices:

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

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

\(\frac{1}{{32}}\)

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

Questions 28 of 50

Question:A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that these are of the same colour is

Answers Choices:

\(\frac{5}{{108}}\)

\(\frac{{18}}{{108}}\)

\(\frac{{30}}{{108}}\)

\(\frac{{48}}{{108}}\)

Questions 29 of 50

Question:A bag contains 3 red, 4 white and 5 blue balls. All balls are different. Two balls are drawn at random. The probability that they are of different colour is

Answers Choices:

\(\frac{{47}}{{66}}\)

\(\frac{{10}}{{33}}\)

\(\frac{5}{{22}}\)

None of these

Questions 30 of 50

Question:Ten students are seated at random in a row. The probability that two particular students are not seated side by side is

Answers Choices:

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

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

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

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

Questions 31 of 50

Question:In a horse race the odds in favour of three horses are \(1:2\), \(1:3\) and \(1:4\). The probability that one of the horse will win the race is

Answers Choices:

\(\frac{{37}}{{60}}\)

\(\frac{{47}}{{60}}\)

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

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

Questions 32 of 50

Question:The odds against a certain event is 5 : 2 and the odds in favour of another event is 6 : 5. If both the events are independent, then the probability that at least one of the events will happen is

Answers Choices:

\(\frac{{50}}{{77}}\)

\(\frac{{52}}{{77}}\)

\(\frac{{25}}{{88}}\)

\(\frac{{63}}{{88}}\)

Questions 33 of 50

Question:If A and B are two mutually exclusive events, then \(P\,(A + B) = \)

Answers Choices:

\(P\,(A) + P\,(B) - P\,(AB)\)

\(P\,(A) - P\,(B)\)

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

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

Questions 34 of 50

Question:The probability of happening at least one of the events A and B is 0.6. If the events A and B happens simultaneously with the probability 0.2, then \(P\,(\bar A) + P\,(\bar B) = \)

Answers Choices:

0.4

0.8

1.2

1.4

Questions 35 of 50

Question:The two events A and B have probabilities 0.25 and 0.50 respectively. The probability that both A and B occur simultaneously is 0.14. Then the probability that neither A nor B occurs is

Answers Choices:

0.39

0.25

0.904

None of these

Questions 36 of 50

Question:Twelve tickets are numbered 1 to 12. One ticket is drawn at random, then the probability of the number to be divisible by 2 or 3, is

Answers Choices:

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

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

\(\frac{5}{6}\)

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

Questions 37 of 50

Question:The probability of solving a question by three students are \(\frac{1}{2},\,\,\frac{1}{4},\,\,\frac{1}{6}\) respectively. Probability of question is being solved will be

Answers Choices:

\(\frac{{33}}{{48}}\)

\(\frac{{35}}{{48}}\)

\(\frac{{31}}{{48}}\)

\(\frac{{37}}{{48}}\)

Questions 38 of 50

Question:Let A and B are two independent events. The probability that both A and B occur together is 1/6 and the probability that neither of them occurs is 1/3. The probability of occurrence of A is

Answers Choices:

0 or 1

\(\frac{1}{2}\) or \(\frac{1}{3}\)

\(\frac{1}{2}\) or \(\frac{1}{4}\)

\(\frac{1}{3}\) or \(\frac{1}{4}\)

Questions 39 of 50

Question:Two dice are thrown. What is the probability that the sum of the numbers appearing on the two dice is 11, if 5 appears on the first

Answers Choices:

\(\frac{1}{{36}}\)

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

\(\frac{5}{6}\)

None of these

Questions 40 of 50

Question:If \(P\,(A) = \frac{1}{2},\,\,P\,(B) = \frac{1}{3}\) and \(P\,(A \cap B) = \frac{1}{4},\) then \(P\,\left( {\frac{B}{A}} \right) = \)

Answers Choices:

1

0

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

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

Questions 41 of 50

Question:A letter is known to have come either from LONDON or CLIFTON; on the postmark only the two consecutive letters ON are legible. The probability that it came from LONDON is

Answers Choices:

\(\frac{5}{{17}}\)

\(\frac{{12}}{{17}}\)

\(\frac{{17}}{{30}}\)

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

Questions 42 of 50

Question:Let \(0 < P(A) < 1\), \(0 < P(B) < 1\) and \(P(A \cup B) = \) \(P(A) + P(B) - P(A)\,P(B).\) Then

Answers Choices:

\(P(B/A) = P(B) - P(A)\)

\(P({A^c} \cup {B^c}) = P({A^c}) + P({B^c})\)

\(P{(A \cup B)^c} = P({A^c})\,P({B^c})\)

\(P(A/B) = P(A)\)

3 and 4 are correct

Questions 43 of 50

Question:8 coins are tossed simultaneously. The probability of getting at least 6 heads is

Answers Choices:

\(\frac{{57}}{{64}}\)

\(\frac{{229}}{{256}}\)

\(\frac{7}{{64}}\)

\(\frac{{37}}{{256}}\)

Questions 44 of 50

Question:In a box containing 100 eggs, 10 eggs are rotten. The probability that out of a sample of 5 eggs none is rotten if the sampling is with replacement is

Answers Choices:

\({\left( {\frac{1}{{10}}} \right)^5}\)

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

\({\left( {\frac{9}{5}} \right)^5}\)

\({\left( {\frac{9}{{10}}} \right)^5}\)

Questions 45 of 50

Question:If X follows a binomial distribution with parameters \(n = 6\) and p. If \(9P\,(X = 4) = P\,(X = 2),\) then \(p = \)

Answers Choices:

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

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

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

1

Questions 46 of 50

Question:A die is tossed thrice. If getting a four is considered a success, then the mean and variance of the probability distribution of the number of successes are

Answers Choices:

\(\frac{1}{2},\,\frac{1}{{12}}\)

\(\frac{1}{6},\,\frac{5}{{12}}\)

\(\frac{5}{6},\,\frac{1}{2}\)

None of these

Questions 47 of 50

Question:The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. What is the probability that out of 5 such bulbs none will fuse after 150 days of use

Answers Choices:

\(1 - {\left( {\frac{{19}}{{20}}} \right)^5}\)

\({\left( {\frac{{19}}{{20}}} \right)^5}\)

\({\left( {\frac{3}{4}} \right)^5}\)

\(90\,{\left( {\frac{1}{4}} \right)^5}\)

Questions 48 of 50

Question:A dice is thrown 5 times, then the probability that an even number will come up exactly 3 times is

Answers Choices:

\(\frac{5}{{16}}\)

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

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

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

Questions 49 of 50

Question:The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, then \(P(X = 1)\) is

Answers Choices:

1/32

1/16

1/8

1/4

Questions 50 of 50

Question:A coin is tossed n times. The probability of getting head at least once is greater than 0.8, then the least value of n is

Answers Choices:

2

3

4

5