# 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

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

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

$$\frac{2}{{25}}$$

$$\frac{9}{{100}}$$

$$\frac{{11}}{{100}}$$

None of these

## Questions 4 of 50

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

$$\frac{1}{2}$$

$$\frac{1}{3}$$

$$\frac{1}{4}$$

None of these

## Questions 5 of 50

Question:The probability of a sure event is

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

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

$$\frac{2}{{663}}$$

$$\frac{2}{{13}}$$

$$\frac{4}{{663}}$$

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

$$\frac{5}{{36}}$$

$$\frac{1}{6}$$

$$\frac{2}{{15}}$$

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

$$\frac{3}{{10}}$$

$$\frac{4}{{10}}$$

$$\frac{3}{6}$$

$$\frac{4}{6}$$

## Questions 10 of 50

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

$$\frac{1}{6}$$

$$\frac{1}{{36}}$$

$$\frac{1}{{18}}$$

$$\frac{3}{{28}}$$

## 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

$$\frac{k}{{999}}$$

$$\frac{k}{{1000}}$$

$$\frac{{k - 1}}{{1000}}$$

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

$$\frac{5}{6}$$

$$\frac{{91}}{{216}}$$

$$\frac{1}{{36}}$$

$$\frac{{125}}{{216}}$$

## 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

$$\frac{1}{5}$$

$$\frac{2}{5}$$

$$\frac{1}{{10}}$$

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

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

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

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

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

$$\frac{2}{{13}}$$

$$\frac{8}{{663}}$$

$$\frac{4}{{663}}$$

$$\frac{{103}}{{663}}$$

## 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

$$\frac{{197}}{{200}}$$

$$\frac{{27}}{{100}}$$

$$\frac{{83}}{{100}}$$

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

$$\frac{1}{6}$$

$$\frac{1}{3}$$

$$\frac{1}{2}$$

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

$$\frac{2}{{13}}$$

$$\frac{1}{{51}}$$

$$\frac{1}{{221}}$$

$$\frac{2}{{21}}$$

## Questions 19 of 50

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

$$\frac{1}{7}$$

$$\frac{2}{7}$$

$$\frac{4}{{53}}$$

$$\frac{4}{{49}}$$

## 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

$$\frac{2}{5}$$

$$\frac{8}{{15}}$$

$$\frac{6}{{11}}$$

$$\frac{2}{3}$$

## 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

$$\frac{1}{{26}}$$

$$\frac{1}{4}$$

$$\frac{1}{{17}}$$

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

$$^{26}{C_6}$$

$$\frac{{^{26}{C_3}}}{{^{52}{C_6}}}$$

$$\frac{{^{26}{C_3}{ \times ^{26}}{C_3}}}{{^{52}{C_6}}}$$

$$\frac{1}{2}$$

## Questions 23 of 50

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

$$\frac{1}{2}$$

$$\frac{1}{{64}}$$

$$\frac{{^8{C_4}}}{8}$$

$$\frac{{^8{C_4}}}{{{2^8}}}$$

## 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

$$\frac{{17}}{{35}}$$

$$\frac{{18}}{{35}}$$

$$\frac{{72}}{{175}}$$

$$\frac{{13}}{{175}}$$

## 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

$$\frac{1}{{5\,!}}$$

$$\frac{{50\,!}}{{55\,!}}$$

$$\frac{1}{{{{50}^5}}}$$

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

$$\frac{7}{{13}}$$

$$\frac{{11}}{{15}}$$

$$\frac{{12}}{{13}}$$

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

$$\frac{{14}}{{29}}$$

$$\frac{{20}}{{39}}$$

$$\frac{1}{2}$$

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

$$\frac{1}{{17}}$$

$$\frac{3}{{19}}$$

$$\frac{2}{{19}}$$

$$\frac{2}{{17}}$$

## 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

$$\frac{{20}}{{204}}$$

$$\frac{5}{{204}}$$

$$\frac{1}{3}$$

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

$$\frac{{15}}{{91}}$$

$$\frac{{30}}{{91}}$$

$$\frac{{20}}{{91}}$$

$$\frac{{24}}{{91}}$$

## 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

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

$$\frac{1}{5}$$

$$\frac{2}{5}$$

$$\frac{3}{5}$$

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

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 =

$$\frac{1}{3}$$

$$\frac{1}{2}$$

$$\frac{2}{3}$$

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

$$p + q$$

$$p + q - 2qp$$

$$p + q - pq$$

$$p + q + pq$$

## 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

$$\frac{1}{2}$$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

$$\frac{{13}}{{25}}$$

$$\frac{3}{{25}}$$

$$\frac{{17}}{{25}}$$

$$\frac{8}{{25}}$$

## Questions 38 of 50

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

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

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

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

None of these

## Questions 39 of 50

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

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

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 $$P\,\left( {\frac{B}{A}} \right) =$$

$$\frac{2}{5}$$

$$\frac{3}{5}$$

$$\frac{7}{{10}}$$

$$\frac{{19}}{{60}}$$

## 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

$$\frac{1}{2}$$

$$\frac{1}{4}$$

$$\frac{1}{3}$$

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

$$\frac{1}{{18}}$$

$$\frac{1}{{36}}$$

$$\frac{1}{9}$$

$$\frac{1}{3}$$

## 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

$$\frac{1}{{19}}$$

$$\frac{2}{{19}}$$

$$\frac{3}{{19}}$$

None of these

## Questions 45 of 50

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

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

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

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

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

## 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

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

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

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

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

## 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

$$^n{C_{n + r}}{p^r}{q^{n - r}}$$

$$^n{C_r}{p^{r - 1}}{q^{r + 1}}$$

$$^n{C_r}{q^{n - r}}{p^r}$$

$$^n{C_r}{p^{r + 1}}{q^{r - 1}}$$

## 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

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

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

$$\mu = 2,\,\,{\sigma ^2} = 2/3$$

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

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

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

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

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

## 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

$$\frac{8}{3}$$
$$\frac{3}{8}$$
$$\frac{4}{5}$$
$$\frac{5}{4}$$