# Probability Test 5

Total Questions:50 Total Time: 75 Min

Remaining:

## Questions 1 of 50

Question:If two balanced dice are tossed once, the probability of the event, that the sum of the integers coming on the upper sides of the two dice is 9, is

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

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

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

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

## Questions 2 of 50

Question:From a well shuffled pack of cards one card is drawn at random. The probability that the card drawn is an ace is

$$\frac{1}{{13}}$$

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

$$\frac{3}{{52}}$$

None of these

## Questions 3 of 50

Question:The probability of getting at least one tail in 4 throws of a coin is

$$\frac{{15}}{{16}}$$

$$\frac{1}{{16}}$$

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

None of these

## Questions 4 of 50

Question:Three letters are to be sent to different persons and addresses on the three envelopes are also written. Without looking at the addresses, the probability that the letters go into the right envelope is equal to

$$\frac{1}{{27}}$$

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

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

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

## Questions 5 of 50

Question:A card is drawn at random from a pack of 52 cards. The probability that the drawn card is a court card i.e. a jack, a queen or a king, is

$$\frac{3}{{52}}$$

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

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

None of these

## Questions 6 of 50

Question:Two dice are thrown together. The probability that sum of the two numbers will be a multiple of 4 is

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

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

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

$$\frac{5}{9}$$

## Questions 7 of 50

Question:Three persons work independently on a problem. If the respective probabilities that they will solve it are 1/3, 1/4 and 1/5, then the probability that none can solve it

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

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

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

None of these

## Questions 8 of 50

Question:Two dice are thrown. The probability that the sum of the points on two dice will be 7, is

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

$$\frac{6}{{36}}$$

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

$$\frac{8}{{36}}$$

## Questions 9 of 50

Question:There are n letters and n addressed envelops. The probability that each letter takes place in right envelop is

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

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

$$1 - \frac{1}{{n\,!}}$$

None of these

## Questions 10 of 50

Question:If the probabilities of boy and girl to be born are same, then in a 4 children family the probability of being at least one girl, is

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

$$\frac{{15}}{{16}}$$

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

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

## Questions 11 of 50

Question:The probability of obtaining sum '8' in a single throw of two dice

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

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

$$\frac{4}{{36}}$$

$$\frac{6}{{36}}$$

## Questions 12 of 50

Question:For any event A

$$P(A) + P(\bar A) = 0$$

$$P(A) + P(\bar A) = 1$$

$$P(A) > 1$$

$$P(\bar A) < 1$$

## Questions 13 of 50

Question:The chances of throwing a total of 3 or 5 or 11 with two dice is

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

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

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

$$\frac{{19}}{{36}}$$

## Questions 14 of 50

Question:A six faced dice is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice. The probability that the sum of two numbers thrown is even, is

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

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

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

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

## Questions 15 of 50

Question:A binary number is made up of 16 bits. The probability of an incorrect bit appearing is p and the errors in different bits are independent of one another. The probability of forming an incorrect number is

$$\frac{p}{{16}}$$

$${p^{16}}$$

$${}^{16}{C_1}{p^{16}}$$

$$1 - {(1 - p)^{16}}$$

## Questions 16 of 50

Question:A coin is tossed 4 times. The probability that at least one head turns up is

$$\frac{1}{{16}}$$

$$\frac{2}{{16}}$$

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

$$\frac{{15}}{{16}}$$

## Questions 17 of 50

Question:The chance of getting a doublet with 2 dice is

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

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

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

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

## Questions 18 of 50

Question:The chance of throwing a total of 7 or 12 with 2 dice, is

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

$$\frac{5}{9}$$

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

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

## Questions 19 of 50

Question:The probabilities of a problem being solved by two students are $$\frac{1}{2},\frac{1}{3}$$. Then the probability of the problem being solved is

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

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

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

1

## Questions 20 of 50

Question:Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is

$$\frac{8}{9}$$

$$\frac{7}{9}$$

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

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

## Questions 21 of 50

Question:A bag contains 4 white, 5 red and 6 black balls. If two balls are drawn at random, then the probability that one of them is white is

$$\frac{{44}}{{105}}$$

$$\frac{{11}}{{105}}$$

$$\frac{{11}}{{21}}$$

None of these

## Questions 22 of 50

Question:A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, then the probability that 2 are white and 1 is red, is

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

$$\frac{7}{{102}}$$

$$\frac{3}{{68}}$$

$$\frac{1}{{13}}$$

## Questions 23 of 50

Question:A bag contains 6 red, 5 white and 4 black balls. Two balls are drawn. The probability that none of them is red, is

$$\frac{{12}}{{35}}$$

$$\frac{6}{{35}}$$

$$\frac{4}{{35}}$$

None of these

## Questions 24 of 50

Question:A bag contains 3 white and 5 black balls. If one ball is drawn, then the probability that it is black, is

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

$$\frac{5}{8}$$

$$\frac{6}{8}$$

$$\frac{{10}}{{20}}$$

## Questions 25 of 50

Question:Six boys and six girls sit in a row randomly. The probability that the six girls sit together

$$\frac{1}{{77}}$$

$$\frac{1}{{132}}$$

$$\frac{1}{{231}}$$

None of these

## Questions 26 of 50

Question:From a group of 7 men and 4 ladies a committee of 6 persons is formed, then the probability that the committee contains 2 ladies is

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

$$\frac{5}{{11}}$$

$$\frac{4}{{11}}$$

$$\frac{3}{{11}}$$

## Questions 27 of 50

Question:A bag contains 5 black balls, 4 white balls and 3 red balls. If a ball is selected randomwise, the probability that it is a black or red ball is

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

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

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

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

## Questions 28 of 50

Question:Out of 30 consecutive numbers, 2 are chosen at random. The probability that their sum is odd, is

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

$$\frac{{16}}{{29}}$$

$$\frac{{15}}{{29}}$$

$$\frac{{10}}{{29}}$$

## Questions 29 of 50

Question:A basket contains 5 apples and 7 oranges and another basket contains 4 apples and 8 oranges. One fruit is picked out from each basket. Find the probability that the fruits are both apples or both oranges

$$\frac{{24}}{{144}}$$

$$\frac{{56}}{{144}}$$

$$\frac{{68}}{{144}}$$

$$\frac{{76}}{{144}}$$

## Questions 30 of 50

Question:Let A and B be two finite sets having m and n elements respectively such that $$m \le n.\,$$ A mapping is selected at random from the set of all mappings from A to B. The probability that the mapping selected is an injection is

$$\frac{{n\,!}}{{(n - m)\,!\,{m^n}}}$$

$$\frac{{n\,!}}{{(n - m)\,!\,{n^m}}}$$

$$\frac{{m\,!}}{{(n - m)\,!\,{n^m}}}$$

$$\frac{{m\,!}}{{(n - m)\,!\,{m^n}}}$$

## Questions 31 of 50

Question:The probabilities of three mutually exclusive events are 2/3, 1/4 and 1/6. The statement is

TRUE

Wrong

Could be either

Do not know

## Questions 32 of 50

Question:If A and B are two events such that $$P(A) = 0.4$$ , $$P\,(A + B) = 0.7$$ and$$P\,(AB) = 0.2,$$ then $$P\,(B) =$$

0.1

0.3

0.5

None of these

## Questions 33 of 50

Question:If an integer is chosen at random from first 100 positive integers, then the probability that the chosen number is a multiple of 4 or 6, is

$$\frac{{41}}{{100}}$$

$$\frac{{33}}{{100}}$$

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

None of these

## Questions 34 of 50

Question:If the probability of a horse A winning a race is 1/4 and the probability of a horse B winning the same race is 1/5, then the probability that either of them will win the race is

$$\frac{1}{{20}}$$

$$\frac{9}{{20}}$$

$$\frac{{11}}{{20}}$$

$$\frac{{19}}{{20}}$$

## Questions 35 of 50

Question:The probability that a man will be alive in 20 years is $$\frac{3}{5}$$ and the probability that his wife will be alive in 20 years is $$\frac{2}{3}$$. Then the probability that at least one will be alive in 20 years, is

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

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

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

None of these

## Questions 36 of 50

Question:Given two mutually exclusive events A and B such that $$P(A) = 0.45$$ and $$P(B) = 0.35,$$ then P (A or B) =

0.1

0.25

0.15

0.8

## Questions 37 of 50

Question:The probability that at least one of the events A and B occurs is 3/5. If A and B occur simultaneously with probability 1/5, then $$P(A') + P(B')$$ is

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

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

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

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

## Questions 38 of 50

Question:If A and B are arbitrary events, then

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

$$P(A \cup B) \le P(A) + P(B)$$

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

None of these

## Questions 39 of 50

Question:If the events A and B are mutually exclusive, then $$P\left( {\frac{A}{B}} \right) =$$

0

1

$$\frac{{P\,(A \cap B)}}{{P\,(A)}}$$

$$\frac{{P\,(A \cap B)}}{{P\,(B)}}$$

## Questions 40 of 50

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

0

1

1/2

1/3

## Questions 41 of 50

Question:A and B are two events such that P = 0.8, P=0.6 and $$P(A \cap B) = 0.5,$$ then the value of $$P\,(A/B)$$ is

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

$$\frac{5}{8}$$

$$\frac{9}{{10}}$$

None of these

## Questions 42 of 50

Question:If $$\bar E$$ and $$\bar F$$ are the complementary events of events E and F respectively and if $$0 < P\,(F) < 1,$$then

$$P\,(E/F) + P\,(\bar E/F) = 1$$

$$P\,(E/F) + P\,(E/\bar F) = 1$$

$$P\,(\bar E/F) + P\,(E/\bar F) = 1$$

$$P\,(E/\bar F) + P\,(\bar E/\bar F) = 1$$

1 and 4 are correct

## Questions 43 of 50

Question:If a dice is thrown 7 times, then the probability of obtaining 5 exactly 4 times is

$$^7{C_4}\,{\left( {\frac{1}{6}} \right)^4}{\left( {\frac{5}{6}} \right)^3}$$

$$^7{C_4}\,{\left( {\frac{1}{6}} \right)^3}{\left( {\frac{5}{6}} \right)^4}$$

$${\left( {\frac{1}{6}} \right)^4}{\left( {\frac{5}{6}} \right)^3}$$

$${\left( {\frac{1}{6}} \right)^3}{\left( {\frac{5}{6}} \right)^4}$$

## Questions 44 of 50

Question:If x denotes the number of sixes in four consecutive throws of a dice, then $$P\,(x = 4)$$ is

$$\frac{1}{{1296}}$$

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

1

$$\frac{{1295}}{{1296}}$$

## Questions 45 of 50

Question:The items produced by a firm are supposed to contain 5% defective items. The probability that a sample of 8 items will contain less than 2 defective items, is

$$\frac{{27}}{{20}}\,{\left( {\frac{{19}}{{20}}} \right)^7}$$

$$\frac{{533}}{{400}}\,{\left( {\frac{{19}}{{20}}} \right)^6}$$

$$\frac{{153}}{{20}}\,{\left( {\frac{1}{{20}}} \right)^7}$$

$$\frac{{35}}{{16}}\,{\left( {\frac{1}{{20}}} \right)^6}$$

## Questions 46 of 50

Question:The probability that a man can hit a target is $$\frac{3}{4}$$. He tries 5 times. The probability that he will hit the target at least three times is

$$\frac{{291}}{{364}}$$

$$\frac{{371}}{{464}}$$

$$\frac{{471}}{{502}}$$

$$\frac{{459}}{{512}}$$

## Questions 47 of 50

Question:The mean and variance of a binomial distribution are 6 and 4. The parameter n is

18

12

10

9

## Questions 48 of 50

Question:Five coins whose faces are marked 2, 3 are tossed. The chance of obtaining a total of 12 is

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

$$\frac{1}{{16}}$$

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

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

## Questions 49 of 50

Question:The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is

$$\frac{{28}}{{256}}$$

$$\frac{{219}}{{256}}$$

$$\frac{{128}}{{256}}$$

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

## Questions 50 of 50

Question:If X has binomial distribution with mean np and variance npq, then $$\frac{{P(X = k)}}{{P(X = k - 1)}}$$ is

$$\frac{{n - k}}{{k - 1}}.\frac{p}{q}$$
$$\frac{{n - k + 1}}{k}.\frac{p}{q}$$
$$\frac{{n + 1}}{k}.\frac{q}{p}$$
$$\frac{{n - 1}}{{k + 1}}.\frac{q}{p}$$