# Probability Test 4

Total Questions:50 Total Time: 75 Min

Remaining:

## Questions 1 of 50

Question:The probability of drawing a white ball from a bag containing 3 black balls and 4 white balls, is

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

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

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

None of these

## Questions 2 of 50

Question:A and B toss a coin alternatively, the first to show a head being the winner. If A starts the game, the chance of his winning is

5/8

1/2

1/3

2/3

## Questions 3 of 50

Question:One card is drawn from each of two ordinary packs of 52 cards. The probability that at least one of them is an ace of heart, is

$$\frac{{103}}{{2704}}$$

$$\frac{1}{{2704}}$$

$$\frac{2}{{52}}$$

$$\frac{{2601}}{{2704}}$$

## Questions 4 of 50

Question:A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, what is the probability that it is rusted or is a nail

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

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

$$\frac{{11}}{{16}}$$

$$\frac{{14}}{{16}}$$

## Questions 5 of 50

Question:Two dice are thrown simultaneously. What is the probability of obtaining sum of the numbers less than 11

$$\frac{{17}}{{18}}$$

$$\frac{1}{{12}}$$

$$\frac{{11}}{{12}}$$

None of these

## Questions 6 of 50

Question:The probability that an ordinary or a non-leap year has 53 sunday, is

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

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

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

None of these

## Questions 7 of 50

Question:A coin is tossed until a head appears or until the coin has been tossed five times. If a head does not occur on the first two tosses, then the probability that the coin will be tossed 5 times is

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

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

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

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

## Questions 8 of 50

Question:Two dice are tossed. The probability that the total score is a prime number is

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

$$\frac{5}{{12}}$$

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

None of these

## Questions 9 of 50

Question:A card is drawn randomly from a pack of playing cards. Then the probability that it is neither ace nor king, is

$$\frac{{11}}{{13}}$$

$$\frac{8}{{13}}$$

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

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

## Questions 10 of 50

Question:There are 4 envelopes with addresses and 4 concerning letters. The probability that letter does not go into concerning proper envelope, is or There are four letters and four addressed envelopes. The chance that all letters are not despatched in the right envelope is

$$\frac{{19}}{{24}}$$

$$\frac{{21}}{{23}}$$

$$\frac{{23}}{{24}}$$

$$\frac{1}{{24}}$$

## Questions 11 of 50

Question:One card is drawn from a pack of 52 cards. The probability that it is a king or diamond is

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

$$\frac{3}{{26}}$$

$$\frac{4}{{13}}$$

$$\frac{3}{{13}}$$

## Questions 12 of 50

Question:A bag contains 3 white, 3 black and 2 red balls. One by one three balls are drawn without replacing them. The probability that the third ball is red, is

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

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

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

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

## Questions 13 of 50

Question:Cards are drawn one by one without replacement from a pack of 52 cards. The probability that 10 cards will precede the first ace is

$$\frac{{241}}{{1456}}$$

$$\frac{{164}}{{4165}}$$

$$\frac{{451}}{{884}}$$

None of these

## Questions 14 of 50

Question:The probability that a teacher will give an unannounced test during any class meeting is 1/5. If a student is absent twice, then the probability that the student will miss at least one test is

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

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

$$\frac{7}{5}$$

$$\frac{9}{{25}}$$

## Questions 15 of 50

Question:An integer is chosen at random and squared. The probability that the last digit of the square is 1 or 5 is

$$\frac{2}{{10}}$$

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

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

$$\frac{9}{{25}}$$

## Questions 16 of 50

Question:Two integers are chosen at random and multiplied. The probability that the product is an even integer is

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

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

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

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

## Questions 17 of 50

Question:Two cards are drawn without replacement from a well-shuffled pack. Find the probability that one of them is an ace of heart

$$\frac{1}{{25}}$$

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

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

None of these

## Questions 18 of 50

Question:A problem in Mathematics is given to three students A, B, C and their respective probability of solving the problem is 1/2, 1/3 and 1/4. Probability that the problem is solved is

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

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

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

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

## Questions 19 of 50

Question:Probability of throwing 16 in one throw with three dice is

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

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

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

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

## Questions 20 of 50

Question:The probability of choosing at random a number that is divisible by 6 or 8 from among 1 to 90 is equal to

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

$$\frac{1}{{30}}$$

$$\frac{{11}}{{80}}$$

$$\frac{{23}}{{90}}$$

## Questions 21 of 50

Question:If Mohan has 3 tickets of a lottery containing 3 prizes and 9 blanks, then his chance of winning prize are

$$\frac{{34}}{{55}}$$

$$\frac{{21}}{{55}}$$

$$\frac{{17}}{{55}}$$

None of these

## Questions 22 of 50

Question:A bag contains 3 white and 7 red balls. If a ball is drawn at random, then what is the probability that the drawn ball is either white or red

0

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

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

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

## Questions 23 of 50

Question:n cadets have to stand in a row. If all possible permutations are equally likely, then the probability that two particular cadets stand side by side, is

$$\frac{2}{n}$$

$$\frac{1}{n}$$

$$\frac{2}{{(n - 1)\,!}}$$

None of these

## Questions 24 of 50

Question:A bag contains tickets numbered from 1 to 20. Two tickets are drawn. The probability that both the numbers are prime, is

$$\frac{{14}}{{95}}$$

$$\frac{7}{{95}}$$

$$\frac{1}{{95}}$$

None of these

## Questions 25 of 50

Question:Dialing a telephone number an old man forgets the last two digits remembering only that these are different dialled at random. The probability that the number is dialled correctly, is

$$\frac{1}{{45}}$$

$$\frac{1}{{90}}$$

$$\frac{1}{{100}}$$

None of these

## Questions 26 of 50

Question:In a box there are 2 red, 3 black and 4 white balls. Out of these three balls are drawn together. The probability of these being of same colour is

$$\frac{1}{{84}}$$

$$\frac{1}{{21}}$$

$$\frac{5}{{84}}$$

None of these

## Questions 27 of 50

Question:In a lottery there were 90 tickets numbered 1 to 90. Five tickets were drawn at random. The probability that two of the tickets drawn numbers 15 and 89 is

$$\frac{2}{{801}}$$

$$\frac{2}{{623}}$$

$$\frac{1}{{267}}$$

$$\frac{1}{{623}}$$

## Questions 28 of 50

Question:Among 15 players, 8 are batsmen and 7 are bowlers. Find the probability that a team is chosen of 6 batsmen and 5 bowlers

$$\frac{{{}^8{C_6} \times {}^7{C_5}}}{{{}^{15}{C_{11}}}}$$

$$\frac{{^8{C_6}{ + ^7}{C_5}}}{{^{15}{C_{11}}}}$$

$$\frac{{15}}{{28}}$$

None of these

## Questions 29 of 50

Question:A bag contains 8 red and 7 black balls. Two balls are drawn at random. The probability that both the balls are of the same colour is

$$\frac{{14}}{{15}}$$

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

$$\frac{7}{{15}}$$

$$\frac{4}{{15}}$$

## Questions 30 of 50

Question:From eighty cards numbered 1 to 80, two cards are selected randomly. The probability that both the cards have the numbers divisible by 4 is given by

$$\frac{{21}}{{316}}$$

$$\frac{{19}}{{316}}$$

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

None of these

## Questions 31 of 50

Question:A party of 23 persons take their seats at a round table. The odds against two persons sitting together are

10:01

1:11

9:10

None of these

## Questions 32 of 50

Question:If two events A and B are such that $$P\,(A + B) = \frac{5}{6},$$ $$P\,(AB) = \frac{1}{3}\,$$and $$P\,(\bar A) = \frac{1}{2},$$ then the events A and B are

Independent

Mutually exclusive

Mutually exclusive and independent

None of these

## Questions 33 of 50

Question:If A and B are two independent events such that $$P\,(A) = 0.40,\,\,P\,(B) = 0.50.$$ Find $$P$$(neither A nor B)

0.9

0.1

0.2

0.3

## Questions 34 of 50

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

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

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

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

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

## Questions 35 of 50

Question:In a city 20% persons read English newspaper, 40% read Hindi newspaper and 5% read both newspapers. The percentage of non-reader either paper is

60%

35%

25%

45%

## Questions 36 of 50

Question:The probability that at least one of A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, then $$P(A') + P(B') =$$

0.9

1.15

1.1

1.2

## Questions 37 of 50

Question:If A and B are any two events, then $$P(\bar A \cap B) =$$

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

$$1 - P(A) - P(B)$$

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

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

## Questions 38 of 50

Question:In two events $$P(A \cup B) = 5/6$$, $$P({A^c}) = 5/6$$, $$P(B) = 2/3,$$ then A and B are

Independent

Mutually exclusive

Mutually exhaustive

Dependent

## Questions 39 of 50

Question:If A and B are two events such that $$P\,(A) = \frac{1}{3}$$, $$P\,(B) = \frac{1}{4}$$ and $$P\,(A \cap B) = \frac{1}{5},$$ then $$P\,\left( {\frac{{\bar B}}{{\bar A}}} \right) =$$

$$\frac{{37}}{{40}}$$

$$\frac{{37}}{{45}}$$

$$\frac{{23}}{{40}}$$

None of these

## Questions 40 of 50

Question:If A and B are two events such that $$P\,(A) = \frac{3}{8},\,$$ $$P\,(B) = \frac{5}{8}$$ and $$P\,(A \cup B) = \frac{3}{4},$$ then$$P\,\left( {\frac{A}{B}} \right) =$$

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

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

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

None of these

## Questions 41 of 50

Question:In an entrance test there are multiple choice questions. There are four possible answers to each question of which one is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then the probability that he was guessing, is

$$\frac{{37}}{{40}}$$

$$\frac{1}{{37}}$$

$$\frac{{36}}{{37}}$$

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

## Questions 42 of 50

Question:A coin is tossed three times in succession. If E is the event that there are at least two heads and F is the event in which first throw is a head, then $$P\,\left( {\frac{E}{F}} \right) =$$

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

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

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

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

## Questions 43 of 50

Question:A fair coin is tossed n times. If the probability that head occurs 6 times is equal to the probability that head occurs 8 times, then n is equal to

15

14

12

7

## Questions 44 of 50

Question:If three dice are thrown together, then the probability of getting 5 on at least one of them is

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

$$\frac{{215}}{{216}}$$

$$\frac{1}{{216}}$$

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

## Questions 45 of 50

Question:In a simultaneous toss of four coins, what is the probability of getting exactly three heads

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

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

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

None of these

## Questions 46 of 50

Question:A coin is tossed successively three times. The probability of getting exactly one head or 2 heads, is

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

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

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

None of these

## Questions 47 of 50

Question:The probability that a student is not a swimmer is 1/5. What is the probability that out of 5 students, 4 are swimmers

$${}^5{C_4}{\left( {\frac{4}{5}} \right)^4}\frac{1}{5}$$

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

$${}^5{C_1}\frac{1}{5}{\left( {\frac{4}{5}} \right)^4} \times {}^5{C_4}$$

None of these

## Questions 48 of 50

Question:An experiment succeeds twice as often as it fails. Find the probability that in 4 trials there will be at least three success

$$\frac{4}{{27}}$$

$$\frac{8}{{27}}$$

$$\frac{{16}}{{27}}$$

$$\frac{{24}}{{27}}$$

## Questions 49 of 50

Question:A coin is tossed 3 times. The probability of obtaining at least two heads is or Three coins are tossed all together. The probability of getting at least two heads is

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

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

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

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

## Questions 50 of 50

Question:A dice is thrown two times. If getting the odd number is considered as success, then the probability of two successes is

$$\frac{1}{2}$$
$$\frac{3}{4}$$
$$\frac{2}{3}$$
$$\frac{1}{4}$$