Total Questions:50 Total Time: 75 Min
Remaining:
Question:Two coins are tossed. Let A be the event that the first coin shows head and B be the event that the second coin shows a tail. Two events A and B are
Mutually exclusive
Dependent
Independent and mutually exclusive
None of these
Question:If \(P\,({A_1} \cup {A_2}) = 1 - P(A_1^c)\,P(A_2^c)\) where c stands for complement, then the events \({A_1}\) and \({A_2}\) are
Independent
Equally likely
Question:From a book containing 100 pages, one page is selected randomly. The probability that the sum of the digits of the page number of the selected page is 11, is
\(\frac{2}{{25}}\)
\(\frac{9}{{100}}\)
\(\frac{{11}}{{100}}\)
Question:There are two childrens in a family. The probability that both of them are boys is
\(\frac{1}{2}\)
\(\frac{1}{3}\)
\(\frac{1}{4}\)
Question:The probability of a sure event is
0
1
2
Question:The probability of happening an event A in one trial is 0.4. The probability that the event A happens at least once in three independent trials is
0.936
0.784
0.904
0.216
Question:Two cards are drawn from a pack of 52 cards. What is the probability that one of them is a queen and the other is an ace
\(\frac{2}{{663}}\)
\(\frac{2}{{13}}\)
\(\frac{4}{{663}}\)
Question:Two dice are thrown together. If the numbers appearing on the two dice are different, then what is the probability that the sum is 6
\(\frac{5}{{36}}\)
\(\frac{1}{6}\)
\(\frac{2}{{15}}\)
Question:From the word `POSSESSIVE', a letter is chosen at random. The probability of it to be S is
\(\frac{3}{{10}}\)
\(\frac{4}{{10}}\)
\(\frac{3}{6}\)
\(\frac{4}{6}\)
Question:Three identical dice are rolled. The probability that same number will appear on each of them will be
\(\frac{1}{{36}}\)
\(\frac{1}{{18}}\)
\(\frac{3}{{28}}\)
Question:A locker can be opened by dialing a fixed three digit code (between 000 and 999). A stranger who does not know the code tries to open the locker by dialing three digits at random. The probability that the stranger succeeds at the \({k^{th}}\) trial is
\(\frac{k}{{999}}\)
\(\frac{k}{{1000}}\)
\(\frac{{k - 1}}{{1000}}\)
Question:In a throw of three dice, the probability that at least one die shows up 1, is
\(\frac{5}{6}\)
\(\frac{{91}}{{216}}\)
\(\frac{{125}}{{216}}\)
Question:A card is drawn at random from a pack of 100 cards numbered 1 to 100. The probability of drawing a number which is a square is
\(\frac{1}{5}\)
\(\frac{2}{5}\)
\(\frac{1}{{10}}\)
Question:Seven chits are numbered 1 to 7. Three are drawn one by one with replacement. The probability that the least number on any selected chit is 5, is
\(1 - {\left( {\frac{2}{7}} \right)^4}\)
\(4\,{\left( {\frac{2}{7}} \right)^4}\)
\({\left( {\frac{3}{7}} \right)^3}\)
Question:From a pack of 52 cards, two cards are drawn one by one without replacement. The probability that first drawn card is a king and second is a queen, is
\(\frac{8}{{663}}\)
\(\frac{{103}}{{663}}\)
Question:The probabilities of a student getting I, II and III division in an examination are respectively \(\frac{1}{{10}},\,\frac{3}{5}\) and \(\frac{1}{4}.\) The probability that the student fails in the examination is
\(\frac{{197}}{{200}}\)
\(\frac{{27}}{{100}}\)
\(\frac{{83}}{{100}}\)
Question:What is the probability that when one die is thrown, the number appearing on top is even
Question:From a pack of 52 cards two cards are drawn in succession one by one without replacement. The probability that both are aces is
\(\frac{1}{{51}}\)
\(\frac{1}{{221}}\)
\(\frac{2}{{21}}\)
Question:The probability that a leap year selected randomly will have 53 Sundays is
\(\frac{1}{7}\)
\(\frac{2}{7}\)
\(\frac{4}{{53}}\)
\(\frac{4}{{49}}\)
Question:A bag contains 3 white and 2 black balls and another bag contains 2 white and 4 black balls. A ball is picked up randomly. The probability of its being black is
\(\frac{8}{{15}}\)
\(\frac{6}{{11}}\)
\(\frac{2}{3}\)
Question:Two cards are drawn at random from a pack of 52 cards. The probability that both are the cards of spade is
\(\frac{1}{{26}}\)
\(\frac{1}{{17}}\)
Question:Six cards are drawn simultaneously from a pack of playing cards. What is the probability that 3 will be red and 3 black
\(^{26}{C_6}\)
\(\frac{{^{26}{C_3}}}{{^{52}{C_6}}}\)
\(\frac{{^{26}{C_3}{ \times ^{26}}{C_3}}}{{^{52}{C_6}}}\)
Question:The probability of getting 4 heads in 8 throws of a coin, is
\(\frac{1}{{64}}\)
\(\frac{{^8{C_4}}}{8}\)
\(\frac{{^8{C_4}}}{{{2^8}}}\)
Question:In a lottery 50 tickets are sold in which 14 are of prize. A man bought 2 tickets, then the probability that the man win the prize, is
\(\frac{{17}}{{35}}\)
\(\frac{{18}}{{35}}\)
\(\frac{{72}}{{175}}\)
\(\frac{{13}}{{175}}\)
Question:There are 5 volumes of Mathematics among 25 books. They are arranged on a shelf in random order. The probability that the volumes of Mathematics stand in increasing order from left to right (the volumes are not necessarily kept side by side) is
\(\frac{1}{{5\,!}}\)
\(\frac{{50\,!}}{{55\,!}}\)
\(\frac{1}{{{{50}^5}}}\)
Question:A cricket team has 15 members, of whom only 5 can bowl. If the names of the 15 members are put into a hat and 11 drawn at random, then the chance of obtaining an eleven containing at least 3 bowlers is
\(\frac{7}{{13}}\)
\(\frac{{11}}{{15}}\)
\(\frac{{12}}{{13}}\)
Question:Out of 40 consecutive natural numbers, two are chosen at random. Probability that the sum of the numbers is odd, is
\(\frac{{14}}{{29}}\)
\(\frac{{20}}{{39}}\)
Question:The probability that the three cards drawn from a pack of 52 cards are all red is
\(\frac{3}{{19}}\)
\(\frac{2}{{19}}\)
\(\frac{2}{{17}}\)
Question:A bag contains 6 white, 7 red and 5 black balls. If 3 balls are drawn from the bag at random, then the probability that all of them are white is
\(\frac{{20}}{{204}}\)
\(\frac{5}{{204}}\)
Question:A bag contains 4 white, 5 red and 6 green balls. Three balls are picked up randomly. The probability that a white, a red and a green ball is drawn is
\(\frac{{15}}{{91}}\)
\(\frac{{30}}{{91}}\)
\(\frac{{20}}{{91}}\)
\(\frac{{24}}{{91}}\)
Question:5 boys and 5 girls are sitting in a row randomly. The probability that boys and girls sit alternatively is
5/126
1/126
4/126
6/125
1/63
Question:If the odds against an event be 2 : 3, then the probability of its occurrence is
\(\frac{3}{5}\)
Question:If the probability of X to fail in the examination is 0.3 and that for Y is 0.2, then the probability that either X or Y fail in the examination is
0.5
0.44
0.6
Question:If \(P\,(A) = 0.4,\,\,P\,(B) = x,\,\,P\,(A \cup B) = 0.7\)and the events A and B are independent, then x =
Question:The probabilities that A and B will die within a year are p and q respectively, then the probability that only one of them will be alive at the end of the year is
\(p + q\)
\(p + q - 2qp\)
\(p + q - pq\)
\(p + q + pq\)
Question:A and B are two independent events. The probability that both A and B occur is \(\frac{1}{6}\) and the probability that neither of them occurs is \(\frac{1}{3}\). Then the probability of the two events are respectively
\(\frac{1}{2}\)and \(\frac{1}{3}\)
\(\frac{1}{5}\)and \(\frac{1}{6}\)
\(\frac{1}{2}\)and \(\frac{1}{6}\)
\(\frac{2}{3}\)and \(\frac{1}{4}\)
Question:In a class of 125 students 70 passed in Mathematics, 55 in Statistics and 30 in both. The probability that a student selected at random from the class has passed in only one subject is
\(\frac{{13}}{{25}}\)
\(\frac{3}{{25}}\)
\(\frac{{17}}{{25}}\)
\(\frac{8}{{25}}\)
Question:A, B, C are any three events. If P (S) denotes the probability of S happening then \(P\,(A \cap (B \cup C)) = \)
\(P(A) + P(B) + P(C) - P(A \cap B) - P(A \cap C)\)
\(P(A) + P(B) + P(C) - P(B)\,P(C)\)
\(P(A \cap B) + P(A \cap C) - P(A \cap B \cap C)\)
Question:If \(P(A \cup B) = 0.8\) and \(P(A \cap B) = 0.3,\) then \(P(\bar A) + P(\bar B) = \)
0.3
0.7
0.9
Question:In a certain population 10% of the people are rich, 5% are famous and 3% are rich and famous. The probability that a person picked at random from the population is either famous or rich but not both, is equal to
0. 07
0.08
0. 09
0. 12
Question:If \(4\,P(A) = 6\,P\,(B) = 10\,P\,(A \cap B) = 1,\) then \(P\,\left( {\frac{B}{A}} \right) = \)
\(\frac{7}{{10}}\)
\(\frac{{19}}{{60}}\)
Question:A pair has two children. If one of them is boy, then the probability that other is also a boy, is
Question:One dice is thrown three times and the sum of the thrown numbers is 15. The probability for which number 4 appears in first throw
\(\frac{1}{9}\)
Question:One ticket is selected at random from 100 tickets numbered 00, 01, 02, ...... 98, 99. If X and Y denote the sum and the product of the digits on the tickets, then \(P\,(X = 9/Y = 0)\) equals
\(\frac{1}{{19}}\)
Question:The binomial distribution for which mean = 6 and variance = 2, is
\({\left( {\frac{2}{3} + \frac{1}{3}} \right)^6}\)
\({\left( {\frac{2}{3} + \frac{1}{3}} \right)^9}\)
\({\left( {\frac{1}{3} + \frac{2}{3}} \right)^6}\)
\({\left( {\frac{1}{3} + \frac{2}{3}} \right)^9}\)
Question:A dice is thrown ten times. If getting even number is considered as a success, then the probability of four successes is
\(^{10}{C_4}{\left( {\frac{1}{2}} \right)^4}\)
\(^{10}{C_4}{\left( {\frac{1}{2}} \right)^6}\)
\(^{10}{C_4}{\left( {\frac{1}{2}} \right)^8}\)
\(^{10}{C_6}{\left( {\frac{1}{2}} \right)^{10}}\)
Question:If there are n independent trials, p and q the probability of success and failure respectively, then probability of exactly r successes or Let p be the probability of happening an event and q its failure, then the total chance of r successes in n trials is
\(^n{C_{n + r}}{p^r}{q^{n - r}}\)
\(^n{C_r}{p^{r - 1}}{q^{r + 1}}\)
\(^n{C_r}{q^{n - r}}{p^r}\)
\(^n{C_r}{p^{r + 1}}{q^{r - 1}}\)
Question:A die is tossed thrice. A success is getting 1 or 6 on a toss. The mean and the variance of number of successes
\(\mu = 1,\,\,{\sigma ^2} = 2/3\)
\(\mu = 2/3,\,\,{\sigma ^2} = 1\)
\(\mu = 2,\,\,{\sigma ^2} = 2/3\)
Question:The mean and variance of a binomial distribution are 4 and 3 respectively, then the probability of getting exactly six successes in this distribution is
\({}^{16}{C_6}{\left( {\frac{1}{4}} \right)^{10}}{\left( {\frac{3}{4}} \right)^6}\)
\({}^{16}{C_6}{\left( {\frac{1}{4}} \right)^6}{\left( {\frac{3}{4}} \right)^{10}}\)
\({}^{12}{C_6}{\left( {\frac{1}{4}} \right)^{10}}{\left( {\frac{3}{4}} \right)^6}\)
\(^{12}{C_6}{\left( {\frac{1}{4}} \right)^6}{\left( {\frac{3}{4}} \right)^6}\)
Question:A die is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is
\(\frac{8}{3}\)
\(\frac{3}{8}\)
\(\frac{4}{5}\)
\(\frac{5}{4}\)