Probability Test 7

Total Questions:50 Total Time: 75 Min

Remaining:

 

Questions 1 of 50

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

Answers Choices:

Mutually exclusive

Dependent

Independent and mutually exclusive

None of these

Questions 2 of 50

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

Answers Choices:

Mutually exclusive

Independent

Equally likely

None of these

Questions 3 of 50

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

Answers Choices:

\(\frac{2}{{25}}\)

\(\frac{9}{{100}}\)

\(\frac{{11}}{{100}}\)

None of these

Questions 4 of 50

Question:There are two childrens in a family. The probability that both of them are boys is

Answers Choices:

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

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

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

None of these

Questions 5 of 50

Question:The probability of a sure event is

Answers Choices:

0

1

2

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

Questions 6 of 50

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

Answers Choices:

0.936

0.784

0.904

0.216

Questions 7 of 50

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

Answers Choices:

\(\frac{2}{{663}}\)

\(\frac{2}{{13}}\)

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

None of these

Questions 8 of 50

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

Answers Choices:

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

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

\(\frac{2}{{15}}\)

None of these

Questions 9 of 50

Question:From the word `POSSESSIVE', a letter is chosen at random. The probability of it to be S is

Answers Choices:

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

\(\frac{4}{{10}}\)

\(\frac{3}{6}\)

\(\frac{4}{6}\)

Questions 10 of 50

Question:Three identical dice are rolled. The probability that same number will appear on each of them will be

Answers Choices:

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

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

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

\(\frac{3}{{28}}\)

Questions 11 of 50

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

Answers Choices:

\(\frac{k}{{999}}\)

\(\frac{k}{{1000}}\)

\(\frac{{k - 1}}{{1000}}\)

None of these

Questions 12 of 50

Question:In a throw of three dice, the probability that at least one die shows up 1, is

Answers Choices:

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

\(\frac{{91}}{{216}}\)

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

\(\frac{{125}}{{216}}\)

Questions 13 of 50

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

Answers Choices:

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

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

\(\frac{1}{{10}}\)

None of these

Questions 14 of 50

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

Answers Choices:

\(1 - {\left( {\frac{2}{7}} \right)^4}\)

\(4\,{\left( {\frac{2}{7}} \right)^4}\)

\({\left( {\frac{3}{7}} \right)^3}\)

None of these

Questions 15 of 50

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

Answers Choices:

\(\frac{2}{{13}}\)

\(\frac{8}{{663}}\)

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

\(\frac{{103}}{{663}}\)

Questions 16 of 50

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

Answers Choices:

\(\frac{{197}}{{200}}\)

\(\frac{{27}}{{100}}\)

\(\frac{{83}}{{100}}\)

None of these

Questions 17 of 50

Question:What is the probability that when one die is thrown, the number appearing on top is even

Answers Choices:

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

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

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

None of these

Questions 18 of 50

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

Answers Choices:

\(\frac{2}{{13}}\)

\(\frac{1}{{51}}\)

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

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

Questions 19 of 50

Question:The probability that a leap year selected randomly will have 53 Sundays is

Answers Choices:

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

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

\(\frac{4}{{53}}\)

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

Questions 20 of 50

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

Answers Choices:

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

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

\(\frac{6}{{11}}\)

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

Questions 21 of 50

Question:Two cards are drawn at random from a pack of 52 cards. The probability that both are the cards of spade is

Answers Choices:

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

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

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

None of these

Questions 22 of 50

Question:Six cards are drawn simultaneously from a pack of playing cards. What is the probability that 3 will be red and 3 black

Answers Choices:

\(^{26}{C_6}\)

\(\frac{{^{26}{C_3}}}{{^{52}{C_6}}}\)

\(\frac{{^{26}{C_3}{ \times ^{26}}{C_3}}}{{^{52}{C_6}}}\)

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

Questions 23 of 50

Question:The probability of getting 4 heads in 8 throws of a coin, is

Answers Choices:

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

\(\frac{1}{{64}}\)

\(\frac{{^8{C_4}}}{8}\)

\(\frac{{^8{C_4}}}{{{2^8}}}\)

Questions 24 of 50

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

Answers Choices:

\(\frac{{17}}{{35}}\)

\(\frac{{18}}{{35}}\)

\(\frac{{72}}{{175}}\)

\(\frac{{13}}{{175}}\)

Questions 25 of 50

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

Answers Choices:

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

\(\frac{{50\,!}}{{55\,!}}\)

\(\frac{1}{{{{50}^5}}}\)

None of these

Questions 26 of 50

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

Answers Choices:

\(\frac{7}{{13}}\)

\(\frac{{11}}{{15}}\)

\(\frac{{12}}{{13}}\)

None of these

Questions 27 of 50

Question:Out of 40 consecutive natural numbers, two are chosen at random. Probability that the sum of the numbers is odd, is

Answers Choices:

\(\frac{{14}}{{29}}\)

\(\frac{{20}}{{39}}\)

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

None of these

Questions 28 of 50

Question:The probability that the three cards drawn from a pack of 52 cards are all red is

Answers Choices:

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

\(\frac{3}{{19}}\)

\(\frac{2}{{19}}\)

\(\frac{2}{{17}}\)

Questions 29 of 50

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

Answers Choices:

\(\frac{{20}}{{204}}\)

\(\frac{5}{{204}}\)

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

None of these

Questions 30 of 50

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

Answers Choices:

\(\frac{{15}}{{91}}\)

\(\frac{{30}}{{91}}\)

\(\frac{{20}}{{91}}\)

\(\frac{{24}}{{91}}\)

Questions 31 of 50

Question:5 boys and 5 girls are sitting in a row randomly. The probability that boys and girls sit alternatively is

Answers Choices:

5/126

1/126

4/126

6/125

1/63

Questions 32 of 50

Question:If the odds against an event be 2 : 3, then the probability of its occurrence is

Answers Choices:

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

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

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

1

Questions 33 of 50

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

Answers Choices:

0.5

0.44

0.6

None of these

Questions 34 of 50

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 =

Answers Choices:

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

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

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

None of these

Questions 35 of 50

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

Answers Choices:

\(p + q\)

\(p + q - 2qp\)

\(p + q - pq\)

\(p + q + pq\)

Questions 36 of 50

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

Answers Choices:

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

\(\frac{1}{5}\)and \(\frac{1}{6}\)

\(\frac{1}{2}\)and \(\frac{1}{6}\)

\(\frac{2}{3}\)and \(\frac{1}{4}\)

Questions 37 of 50

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

Answers Choices:

\(\frac{{13}}{{25}}\)

\(\frac{3}{{25}}\)

\(\frac{{17}}{{25}}\)

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

Questions 38 of 50

Question:A, B, C are any three events. If P (S) denotes the probability of S happening then \(P\,(A \cap (B \cup C)) = \)

Answers Choices:

\(P(A) + P(B) + P(C) - P(A \cap B) - P(A \cap C)\)

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

\(P(A \cap B) + P(A \cap C) - P(A \cap B \cap C)\)

None of these

Questions 39 of 50

Question:If \(P(A \cup B) = 0.8\) and \(P(A \cap B) = 0.3,\) then \(P(\bar A) + P(\bar B) = \)

Answers Choices:

0.3

0.5

0.7

0.9

Questions 40 of 50

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

Answers Choices:

0. 07

0.08

0. 09

0. 12

Questions 41 of 50

Question:If \(4\,P(A) = 6\,P\,(B) = 10\,P\,(A \cap B) = 1,\) then \(P\,\left( {\frac{B}{A}} \right) = \)

Answers Choices:

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

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

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

\(\frac{{19}}{{60}}\)

Questions 42 of 50

Question:A pair has two children. If one of them is boy, then the probability that other is also a boy, is

Answers Choices:

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

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

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

None of these

Questions 43 of 50

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

Answers Choices:

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

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

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

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

Questions 44 of 50

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

Answers Choices:

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

\(\frac{2}{{19}}\)

\(\frac{3}{{19}}\)

None of these

Questions 45 of 50

Question:The binomial distribution for which mean = 6 and variance = 2, is

Answers Choices:

\({\left( {\frac{2}{3} + \frac{1}{3}} \right)^6}\)

\({\left( {\frac{2}{3} + \frac{1}{3}} \right)^9}\)

\({\left( {\frac{1}{3} + \frac{2}{3}} \right)^6}\)

\({\left( {\frac{1}{3} + \frac{2}{3}} \right)^9}\)

Questions 46 of 50

Question:A dice is thrown ten times. If getting even number is considered as a success, then the probability of four successes is

Answers Choices:

\(^{10}{C_4}{\left( {\frac{1}{2}} \right)^4}\)

\(^{10}{C_4}{\left( {\frac{1}{2}} \right)^6}\)

\(^{10}{C_4}{\left( {\frac{1}{2}} \right)^8}\)

\(^{10}{C_6}{\left( {\frac{1}{2}} \right)^{10}}\)

Questions 47 of 50

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

Answers Choices:

\(^n{C_{n + r}}{p^r}{q^{n - r}}\)

\(^n{C_r}{p^{r - 1}}{q^{r + 1}}\)

\(^n{C_r}{q^{n - r}}{p^r}\)

\(^n{C_r}{p^{r + 1}}{q^{r - 1}}\)

Questions 48 of 50

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

Answers Choices:

\(\mu = 1,\,\,{\sigma ^2} = 2/3\)

\(\mu = 2/3,\,\,{\sigma ^2} = 1\)

\(\mu = 2,\,\,{\sigma ^2} = 2/3\)

None of these

Questions 49 of 50

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

Answers Choices:

\({}^{16}{C_6}{\left( {\frac{1}{4}} \right)^{10}}{\left( {\frac{3}{4}} \right)^6}\)

\({}^{16}{C_6}{\left( {\frac{1}{4}} \right)^6}{\left( {\frac{3}{4}} \right)^{10}}\)

\({}^{12}{C_6}{\left( {\frac{1}{4}} \right)^{10}}{\left( {\frac{3}{4}} \right)^6}\)

\(^{12}{C_6}{\left( {\frac{1}{4}} \right)^6}{\left( {\frac{3}{4}} \right)^6}\)

Questions 50 of 50

Question:A die is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is

Answers Choices:

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

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

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

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