Total Questions:50 Total Time: 75 Min
Remaining:
Question:If two balanced dice are tossed once, the probability of the event, that the sum of the integers coming on the upper sides of the two dice is 9, is
\(\frac{7}{{18}}\)
\(\frac{5}{{36}}\)
\(\frac{1}{9}\)
\(\frac{1}{6}\)
Question:From a well shuffled pack of cards one card is drawn at random. The probability that the card drawn is an ace is
\(\frac{1}{{13}}\)
\(\frac{4}{{13}}\)
\(\frac{3}{{52}}\)
None of these
Question:The probability of getting at least one tail in 4 throws of a coin is
\(\frac{{15}}{{16}}\)
\(\frac{1}{{16}}\)
\(\frac{1}{4}\)
Question:Three letters are to be sent to different persons and addresses on the three envelopes are also written. Without looking at the addresses, the probability that the letters go into the right envelope is equal to
\(\frac{1}{{27}}\)
\(\frac{4}{{27}}\)
Question:A card is drawn at random from a pack of 52 cards. The probability that the drawn card is a court card i.e. a jack, a queen or a king, is
\(\frac{3}{{13}}\)
Question:Two dice are thrown together. The probability that sum of the two numbers will be a multiple of 4 is
\(\frac{1}{3}\)
\(\frac{5}{9}\)
Question:Three persons work independently on a problem. If the respective probabilities that they will solve it are 1/3, 1/4 and 1/5, then the probability that none can solve it
\(\frac{2}{5}\)
\(\frac{3}{5}\)
Question:Two dice are thrown. The probability that the sum of the points on two dice will be 7, is
\(\frac{6}{{36}}\)
\(\frac{7}{{36}}\)
\(\frac{8}{{36}}\)
Question:There are n letters and n addressed envelops. The probability that each letter takes place in right envelop is
\(\frac{1}{{n\,!}}\)
\(\frac{1}{{(n - 1)\,!}}\)
\(1 - \frac{1}{{n\,!}}\)
Question:If the probabilities of boy and girl to be born are same, then in a 4 children family the probability of being at least one girl, is
\(\frac{{14}}{{16}}\)
\(\frac{1}{8}\)
\(\frac{3}{8}\)
Question:The probability of obtaining sum '8' in a single throw of two dice
\(\frac{1}{{36}}\)
\(\frac{4}{{36}}\)
Question:For any event A
\(P(A) + P(\bar A) = 0\)
\(P(A) + P(\bar A) = 1\)
\(P(A) > 1\)
\(P(\bar A) < 1\)
Question:The chances of throwing a total of 3 or 5 or 11 with two dice is
\(\frac{2}{9}\)
\(\frac{{19}}{{36}}\)
Question:A six faced dice is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice. The probability that the sum of two numbers thrown is even, is
\(\frac{1}{{12}}\)
\(\frac{2}{3}\)
Question:A binary number is made up of 16 bits. The probability of an incorrect bit appearing is p and the errors in different bits are independent of one another. The probability of forming an incorrect number is
\(\frac{p}{{16}}\)
\({p^{16}}\)
\({}^{16}{C_1}{p^{16}}\)
\(1 - {(1 - p)^{16}}\)
Question:A coin is tossed 4 times. The probability that at least one head turns up is
\(\frac{2}{{16}}\)
Question:The chance of getting a doublet with 2 dice is
\(\frac{5}{6}\)
Question:The chance of throwing a total of 7 or 12 with 2 dice, is
Question:The probabilities of a problem being solved by two students are \(\frac{1}{2},\frac{1}{3}\). Then the probability of the problem being solved is
\(\frac{4}{3}\)
1
Question:Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is
\(\frac{8}{9}\)
\(\frac{7}{9}\)
Question:A bag contains 4 white, 5 red and 6 black balls. If two balls are drawn at random, then the probability that one of them is white is
\(\frac{{44}}{{105}}\)
\(\frac{{11}}{{105}}\)
\(\frac{{11}}{{21}}\)
Question:A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, then the probability that 2 are white and 1 is red, is
\(\frac{5}{{204}}\)
\(\frac{7}{{102}}\)
\(\frac{3}{{68}}\)
Question:A bag contains 6 red, 5 white and 4 black balls. Two balls are drawn. The probability that none of them is red, is
\(\frac{{12}}{{35}}\)
\(\frac{6}{{35}}\)
\(\frac{4}{{35}}\)
Question:A bag contains 3 white and 5 black balls. If one ball is drawn, then the probability that it is black, is
\(\frac{5}{8}\)
\(\frac{6}{8}\)
\(\frac{{10}}{{20}}\)
Question:Six boys and six girls sit in a row randomly. The probability that the six girls sit together
\(\frac{1}{{77}}\)
\(\frac{1}{{132}}\)
\(\frac{1}{{231}}\)
Question:From a group of 7 men and 4 ladies a committee of 6 persons is formed, then the probability that the committee contains 2 ladies is
\(\frac{5}{{13}}\)
\(\frac{5}{{11}}\)
\(\frac{4}{{11}}\)
\(\frac{3}{{11}}\)
Question:A bag contains 5 black balls, 4 white balls and 3 red balls. If a ball is selected randomwise, the probability that it is a black or red ball is
\(\frac{5}{{12}}\)
Question:Out of 30 consecutive numbers, 2 are chosen at random. The probability that their sum is odd, is
\(\frac{{14}}{{29}}\)
\(\frac{{16}}{{29}}\)
\(\frac{{15}}{{29}}\)
\(\frac{{10}}{{29}}\)
Question:A basket contains 5 apples and 7 oranges and another basket contains 4 apples and 8 oranges. One fruit is picked out from each basket. Find the probability that the fruits are both apples or both oranges
\(\frac{{24}}{{144}}\)
\(\frac{{56}}{{144}}\)
\(\frac{{68}}{{144}}\)
\(\frac{{76}}{{144}}\)
Question:Let A and B be two finite sets having m and n elements respectively such that \(m \le n.\,\) A mapping is selected at random from the set of all mappings from A to B. The probability that the mapping selected is an injection is
\(\frac{{n\,!}}{{(n - m)\,!\,{m^n}}}\)
\(\frac{{n\,!}}{{(n - m)\,!\,{n^m}}}\)
\(\frac{{m\,!}}{{(n - m)\,!\,{n^m}}}\)
\(\frac{{m\,!}}{{(n - m)\,!\,{m^n}}}\)
Question:The probabilities of three mutually exclusive events are 2/3, 1/4 and 1/6. The statement is
TRUE
Wrong
Could be either
Do not know
Question:If A and B are two events such that \(P(A) = 0.4\) , \(P\,(A + B) = 0.7\) and\(P\,(AB) = 0.2,\) then \(P\,(B) = \)
0.1
0.3
0.5
Question:If an integer is chosen at random from first 100 positive integers, then the probability that the chosen number is a multiple of 4 or 6, is
\(\frac{{41}}{{100}}\)
\(\frac{{33}}{{100}}\)
\(\frac{1}{{10}}\)
Question:If the probability of a horse A winning a race is 1/4 and the probability of a horse B winning the same race is 1/5, then the probability that either of them will win the race is
\(\frac{1}{{20}}\)
\(\frac{9}{{20}}\)
\(\frac{{11}}{{20}}\)
\(\frac{{19}}{{20}}\)
Question:The probability that a man will be alive in 20 years is \(\frac{3}{5}\) and the probability that his wife will be alive in 20 years is \(\frac{2}{3}\). Then the probability that at least one will be alive in 20 years, is
\(\frac{{13}}{{15}}\)
\(\frac{7}{{15}}\)
\(\frac{4}{{15}}\)
Question:Given two mutually exclusive events A and B such that \(P(A) = 0.45\) and \(P(B) = 0.35,\) then P (A or B) =
0.25
0.15
0.8
Question:The probability that at least one of the events A and B occurs is 3/5. If A and B occur simultaneously with probability 1/5, then \(P(A') + P(B')\) is
\(\frac{4}{5}\)
\(\frac{6}{5}\)
\(\frac{7}{5}\)
Question:If A and B are arbitrary events, then
\(P(A \cap B) \ge P(A) + P(B)\)
\(P(A \cup B) \le P(A) + P(B)\)
\(P(A \cap B) = P(A) + P(B)\)
Question:If the events A and B are mutually exclusive, then \(P\left( {\frac{A}{B}} \right) = \)
0
\(\frac{{P\,(A \cap B)}}{{P\,(A)}}\)
\(\frac{{P\,(A \cap B)}}{{P\,(B)}}\)
Question:If A and B are two events such that \(A \subseteq B,\) then \(P\,\left( {\frac{B}{A}} \right) = \)
1/2
1/3
Question:A and B are two events such that P = 0.8, P=0.6 and \(P(A \cap B) = 0.5,\) then the value of \(P\,(A/B)\) is
\(\frac{9}{{10}}\)
Question:If \(\bar E\) and \(\bar F\) are the complementary events of events E and F respectively and if \(0 < P\,(F) < 1,\)then
\(P\,(E/F) + P\,(\bar E/F) = 1\)
\(P\,(E/F) + P\,(E/\bar F) = 1\)
\(P\,(\bar E/F) + P\,(E/\bar F) = 1\)
\(P\,(E/\bar F) + P\,(\bar E/\bar F) = 1\)
1 and 4 are correct
Question:If a dice is thrown 7 times, then the probability of obtaining 5 exactly 4 times is
\(^7{C_4}\,{\left( {\frac{1}{6}} \right)^4}{\left( {\frac{5}{6}} \right)^3}\)
\(^7{C_4}\,{\left( {\frac{1}{6}} \right)^3}{\left( {\frac{5}{6}} \right)^4}\)
\({\left( {\frac{1}{6}} \right)^4}{\left( {\frac{5}{6}} \right)^3}\)
\({\left( {\frac{1}{6}} \right)^3}{\left( {\frac{5}{6}} \right)^4}\)
Question:If x denotes the number of sixes in four consecutive throws of a dice, then \(P\,(x = 4)\) is
\(\frac{1}{{1296}}\)
\(\frac{4}{6}\)
\(\frac{{1295}}{{1296}}\)
Question:The items produced by a firm are supposed to contain 5% defective items. The probability that a sample of 8 items will contain less than 2 defective items, is
\(\frac{{27}}{{20}}\,{\left( {\frac{{19}}{{20}}} \right)^7}\)
\(\frac{{533}}{{400}}\,{\left( {\frac{{19}}{{20}}} \right)^6}\)
\(\frac{{153}}{{20}}\,{\left( {\frac{1}{{20}}} \right)^7}\)
\(\frac{{35}}{{16}}\,{\left( {\frac{1}{{20}}} \right)^6}\)
Question:The probability that a man can hit a target is \(\frac{3}{4}\). He tries 5 times. The probability that he will hit the target at least three times is
\(\frac{{291}}{{364}}\)
\(\frac{{371}}{{464}}\)
\(\frac{{471}}{{502}}\)
\(\frac{{459}}{{512}}\)
Question:The mean and variance of a binomial distribution are 6 and 4. The parameter n is
18
12
10
9
Question:Five coins whose faces are marked 2, 3 are tossed. The chance of obtaining a total of 12 is
\(\frac{1}{{32}}\)
\(\frac{3}{{16}}\)
\(\frac{5}{{16}}\)
Question:The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is
\(\frac{{28}}{{256}}\)
\(\frac{{219}}{{256}}\)
\(\frac{{128}}{{256}}\)
\(\frac{{37}}{{256}}\)
Question:If X has binomial distribution with mean np and variance npq, then \(\frac{{P(X = k)}}{{P(X = k - 1)}}\) is
\(\frac{{n - k}}{{k - 1}}.\frac{p}{q}\)
\(\frac{{n - k + 1}}{k}.\frac{p}{q}\)
\(\frac{{n + 1}}{k}.\frac{q}{p}\)
\(\frac{{n - 1}}{{k + 1}}.\frac{q}{p}\)