# Probability Test 2

Total Questions:50 Total Time: 75 Min

Remaining:

## Questions 1 of 50

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

## Questions 2 of 50

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

## Questions 3 of 50

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

## Questions 4 of 50

Question:Two dice are thrown simultaneously. The probability of getting the sum 2 or 8 or 12 is

$$\frac{5}{{18}}$$

$$\frac{7}{{36}}$$

$$\frac{7}{{18}}$$

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

## Questions 5 of 50

Question:The probability of getting number 5 in throwing a dice is

1

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

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

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

## Questions 6 of 50

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

$$\frac{1}{{52}}$$

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

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

None of these

## Questions 7 of 50

Question:In a single throw of two dice what is the probability of getting a total 13

0

1

$$\frac{{13}}{{36}}$$

$$\frac{{25}}{{36}}$$

## Questions 8 of 50

Question:Three dice are thrown simultaneously. What is the probability of obtaining a total of 17 or 18

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

$$\frac{1}{{72}}$$

$$\frac{1}{{54}}$$

None of these

## Questions 9 of 50

Question:If A is a sure event, then the value of P (A not ) is

0

1

1

None of these

## Questions 10 of 50

Question:A number is chosen at random from first ten natural numbers. The probability that number is odd and perfect square is

$$\frac{2}{9}$$

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

$$\frac{3}{7}$$

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

## Questions 11 of 50

Question:In a single throw of two dice, the probability of obtaining a total of 7 or 9, is

$$\frac{5}{{18}}$$

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

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

None of these

## Questions 12 of 50

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

$$\frac{9}{{19}}$$

$$\frac{8}{{18}}$$

$$\frac{9}{{18}}$$

$$\frac{4}{{19}}$$

## Questions 13 of 50

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

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

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

$$\frac{4}{7}$$

$$\frac{{12}}{{49}}$$

## Questions 14 of 50

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

$$\frac{1}{{144}}$$

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

$$\frac{5}{{144}}$$

$$\frac{7}{{144}}$$

## Questions 15 of 50

Question:A fair coin is tossed repeatedly. If tail appears on first four tosses then the probability of head appearing on fifth toss equals

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

$$\frac{1}{{32}}$$

$$\frac{{31}}{{32}}$$

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

## Questions 16 of 50

Question:A coin is tossed 3 times by 2 persons. What is the probability that both get equal number of heads

$$\frac{3}{8}$$

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

$$\frac{5}{{16}}$$

None of these

## Questions 17 of 50

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

$$\frac{4}{{625}}$$

$$\frac{{18}}{{625}}$$

$$\frac{{16}}{{625}}$$

None of these

## Questions 18 of 50

Question:If a coin be tossed n times then probability that the head comes odd times is

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

$$\frac{1}{{{2^n}}}$$

$$\frac{1}{{{2^{n - 1}}}}$$

None of these

## Questions 19 of 50

Question:Four coins are tossed. The probability that at least one head turns up, is

1/16

1/4

15/16

None of these

## Questions 20 of 50

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

$$\frac{4}{5}$$

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

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

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

## Questions 21 of 50

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

$$\frac{{11}}{{50}}$$

$$\frac{{13}}{{50}}$$

$$\frac{{37}}{{50}}$$

None of these

## Questions 22 of 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

$$\frac{{22}}{{145}}$$

$$\frac{{13}}{{15}}$$

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

None of these

## Questions 23 of 50

Question:Word "UNIVERSITY" is arranged randomly. Then the probability that both "I" does not come together, is

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

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

$$\frac{4}{5}$$

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

## Questions 24 of 50

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

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

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

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

None of these

## Questions 25 of 50

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

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

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

$$\frac{5}{{18}}$$

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

## Questions 26 of 50

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

$$\frac{{25}}{{39}}$$

$$\frac{{14}}{{39}}$$

$$\frac{5}{{13}}$$

$$\frac{{10}}{{13}}$$

## Questions 27 of 50

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

$$\frac{1}{8}$$

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

$$\frac{1}{{32}}$$

$$\frac{1}{{35}}$$

## Questions 28 of 50

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

$$\frac{5}{{108}}$$

$$\frac{{18}}{{108}}$$

$$\frac{{30}}{{108}}$$

$$\frac{{48}}{{108}}$$

## Questions 29 of 50

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

$$\frac{{47}}{{66}}$$

$$\frac{{10}}{{33}}$$

$$\frac{5}{{22}}$$

None of these

## Questions 30 of 50

Question:Ten students are seated at random in a row. The probability that two particular students are not seated side by side is

$$\frac{4}{5}$$

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

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

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

## Questions 31 of 50

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

$$\frac{{37}}{{60}}$$

$$\frac{{47}}{{60}}$$

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

$$\frac{3}{4}$$

## Questions 32 of 50

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

$$\frac{{50}}{{77}}$$

$$\frac{{52}}{{77}}$$

$$\frac{{25}}{{88}}$$

$$\frac{{63}}{{88}}$$

## Questions 33 of 50

Question:If A and B are two mutually exclusive events, then $$P\,(A + B) =$$

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

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

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

$$P\,(A) + P\,(B) + P\,(AB)$$

## Questions 34 of 50

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

## Questions 35 of 50

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

None of these

## Questions 36 of 50

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

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

$$\frac{7}{{12}}$$

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

$$\frac{3}{4}$$

## Questions 37 of 50

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

$$\frac{{33}}{{48}}$$

$$\frac{{35}}{{48}}$$

$$\frac{{31}}{{48}}$$

$$\frac{{37}}{{48}}$$

## Questions 38 of 50

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

## Questions 39 of 50

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

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

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

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

None of these

## Questions 40 of 50

Question:If $$P\,(A) = \frac{1}{2},\,\,P\,(B) = \frac{1}{3}$$ and $$P\,(A \cap B) = \frac{1}{4},$$ then $$P\,\left( {\frac{B}{A}} \right) =$$

1

0

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

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

## Questions 41 of 50

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

$$\frac{5}{{17}}$$

$$\frac{{12}}{{17}}$$

$$\frac{{17}}{{30}}$$

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

## Questions 42 of 50

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

## Questions 43 of 50

Question:8 coins are tossed simultaneously. The probability of getting at least 6 heads is

$$\frac{{57}}{{64}}$$

$$\frac{{229}}{{256}}$$

$$\frac{7}{{64}}$$

$$\frac{{37}}{{256}}$$

## Questions 44 of 50

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

$${\left( {\frac{1}{{10}}} \right)^5}$$

$${\left( {\frac{1}{5}} \right)^5}$$

$${\left( {\frac{9}{5}} \right)^5}$$

$${\left( {\frac{9}{{10}}} \right)^5}$$

## Questions 45 of 50

Question:If X follows a binomial distribution with parameters $$n = 6$$ and p. If $$9P\,(X = 4) = P\,(X = 2),$$ then $$p =$$

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

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

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

1

## Questions 46 of 50

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

$$\frac{1}{2},\,\frac{1}{{12}}$$

$$\frac{1}{6},\,\frac{5}{{12}}$$

$$\frac{5}{6},\,\frac{1}{2}$$

None of these

## Questions 47 of 50

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

$$1 - {\left( {\frac{{19}}{{20}}} \right)^5}$$

$${\left( {\frac{{19}}{{20}}} \right)^5}$$

$${\left( {\frac{3}{4}} \right)^5}$$

$$90\,{\left( {\frac{1}{4}} \right)^5}$$

## Questions 48 of 50

Question:A dice is thrown 5 times, then the probability that an even number will come up exactly 3 times is

$$\frac{5}{{16}}$$

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

$$\frac{3}{{16}}$$

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

## Questions 49 of 50

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

1/16

1/8

1/4

## Questions 50 of 50

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