Total Questions:50 Total Time: 75 Min
Remaining:
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
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
Question:If \(P(A) = 2/3\), \(P(B) = 1/2\) and \({\rm{ }}P(A \cup B) = 5/6\) then events A and B are
Mutually exclusive
Independent as well as mutually exhaustive
Independent
Dependent only on A
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
\(\frac{1}{{26}}\)
\(\frac{{17}}{{2704}}\)
\(\frac{1}{{52}}\)
None of these
Question:Two dice are thrown simultaneously. The probability of getting the sum 2 or 8 or 12 is
\(\frac{5}{{18}}\)
\(\frac{7}{{36}}\)
\(\frac{7}{{18}}\)
\(\frac{5}{{36}}\)
Question:The probability of getting number 5 in throwing a dice is
1
\(\frac{1}{3}\)
\(\frac{1}{6}\)
\(\frac{5}{6}\)
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
\(\frac{1}{{18}}\)
Question:In a single throw of two dice what is the probability of getting a total 13
0
\(\frac{{13}}{{36}}\)
\(\frac{{25}}{{36}}\)
Question:Three dice are thrown simultaneously. What is the probability of obtaining a total of 17 or 18
\(\frac{1}{9}\)
\(\frac{1}{{72}}\)
\(\frac{1}{{54}}\)
Question:If A is a sure event, then the value of P (A not ) is
Question:A number is chosen at random from first ten natural numbers. The probability that number is odd and perfect square is
\(\frac{2}{9}\)
\(\frac{2}{5}\)
\(\frac{3}{7}\)
\(\frac{1}{5}\)
Question:In a single throw of two dice, the probability of obtaining a total of 7 or 9, is
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
\(\frac{9}{{19}}\)
\(\frac{8}{{18}}\)
\(\frac{9}{{18}}\)
\(\frac{4}{{19}}\)
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
\(\frac{4}{{49}}\)
\(\frac{1}{7}\)
\(\frac{4}{7}\)
\(\frac{{12}}{{49}}\)
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
\(\frac{1}{{144}}\)
\(\frac{1}{4}\)
\(\frac{5}{{144}}\)
\(\frac{7}{{144}}\)
Question:A fair coin is tossed repeatedly. If tail appears on first four tosses then the probability of head appearing on fifth toss equals
\(\frac{1}{2}\)
\(\frac{1}{{32}}\)
\(\frac{{31}}{{32}}\)
Question:A coin is tossed 3 times by 2 persons. What is the probability that both get equal number of heads
\(\frac{3}{8}\)
\(\frac{5}{{16}}\)
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
\(\frac{4}{{625}}\)
\(\frac{{18}}{{625}}\)
\(\frac{{16}}{{625}}\)
Question:If a coin be tossed n times then probability that the head comes odd times is
\(\frac{1}{{{2^n}}}\)
\(\frac{1}{{{2^{n - 1}}}}\)
Question:Four coins are tossed. The probability that at least one head turns up, is
1/16
1/4
15/16
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
\(\frac{4}{5}\)
\(\frac{3}{5}\)
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
\(\frac{{11}}{{50}}\)
\(\frac{{13}}{{50}}\)
\(\frac{{37}}{{50}}\)
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
\(\frac{{22}}{{145}}\)
\(\frac{{13}}{{15}}\)
Question:Word "UNIVERSITY" is arranged randomly. Then the probability that both "I" does not come together, is
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
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
\(\frac{8}{{15}}\)
\(\frac{2}{3}\)
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
\(\frac{{25}}{{39}}\)
\(\frac{{14}}{{39}}\)
\(\frac{5}{{13}}\)
\(\frac{{10}}{{13}}\)
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
\(\frac{1}{8}\)
\(\frac{2}{{21}}\)
\(\frac{1}{{35}}\)
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
\(\frac{5}{{108}}\)
\(\frac{{18}}{{108}}\)
\(\frac{{30}}{{108}}\)
\(\frac{{48}}{{108}}\)
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
\(\frac{{47}}{{66}}\)
\(\frac{{10}}{{33}}\)
\(\frac{5}{{22}}\)
Question:Ten students are seated at random in a row. The probability that two particular students are not seated side by side is
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
\(\frac{{37}}{{60}}\)
\(\frac{{47}}{{60}}\)
\(\frac{3}{4}\)
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
\(\frac{{50}}{{77}}\)
\(\frac{{52}}{{77}}\)
\(\frac{{25}}{{88}}\)
\(\frac{{63}}{{88}}\)
Question:If A and B are two mutually exclusive events, then \(P\,(A + B) = \)
\(P\,(A) + P\,(B) - P\,(AB)\)
\(P\,(A) - P\,(B)\)
\(P\,(A) + P\,(B)\)
\(P\,(A) + P\,(B) + P\,(AB)\)
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 \(P\,(\bar A) + P\,(\bar B) = \)
0.4
0.8
1.2
1.4
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
0.39
0.25
0.904
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
\(\frac{7}{{12}}\)
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
\(\frac{{33}}{{48}}\)
\(\frac{{35}}{{48}}\)
\(\frac{{31}}{{48}}\)
\(\frac{{37}}{{48}}\)
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
0 or 1
\(\frac{1}{2}\) or \(\frac{1}{3}\)
\(\frac{1}{2}\) or \(\frac{1}{4}\)
\(\frac{1}{3}\) or \(\frac{1}{4}\)
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
\(\frac{1}{{36}}\)
Question:If \(P\,(A) = \frac{1}{2},\,\,P\,(B) = \frac{1}{3}\) and \(P\,(A \cap B) = \frac{1}{4},\) then \(P\,\left( {\frac{B}{A}} \right) = \)
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
\(\frac{5}{{17}}\)
\(\frac{{12}}{{17}}\)
\(\frac{{17}}{{30}}\)
Question:Let \(0 < P(A) < 1\), \(0 < P(B) < 1\) and \(P(A \cup B) = \) \(P(A) + P(B) - P(A)\,P(B).\) Then
\(P(B/A) = P(B) - P(A)\)
\(P({A^c} \cup {B^c}) = P({A^c}) + P({B^c})\)
\(P{(A \cup B)^c} = P({A^c})\,P({B^c})\)
\(P(A/B) = P(A)\)
3 and 4 are correct
Question:8 coins are tossed simultaneously. The probability of getting at least 6 heads is
\(\frac{{57}}{{64}}\)
\(\frac{{229}}{{256}}\)
\(\frac{7}{{64}}\)
\(\frac{{37}}{{256}}\)
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
\({\left( {\frac{1}{{10}}} \right)^5}\)
\({\left( {\frac{1}{5}} \right)^5}\)
\({\left( {\frac{9}{5}} \right)^5}\)
\({\left( {\frac{9}{{10}}} \right)^5}\)
Question:If X follows a binomial distribution with parameters \(n = 6\) and p. If \(9P\,(X = 4) = P\,(X = 2),\) then \(p = \)
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
\(\frac{1}{2},\,\frac{1}{{12}}\)
\(\frac{1}{6},\,\frac{5}{{12}}\)
\(\frac{5}{6},\,\frac{1}{2}\)
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
\(1 - {\left( {\frac{{19}}{{20}}} \right)^5}\)
\({\left( {\frac{{19}}{{20}}} \right)^5}\)
\({\left( {\frac{3}{4}} \right)^5}\)
\(90\,{\left( {\frac{1}{4}} \right)^5}\)
Question:A dice is thrown 5 times, then the probability that an even number will come up exactly 3 times is
\(\frac{3}{{16}}\)
\(\frac{3}{2}\)
Question:The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, then \(P(X = 1)\) is
1/32
1/8
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
2
3
4
5