Probability Test 1

Total Questions:50 Total Time: 75 Min

Remaining:

 

Questions 1 of 50

Question:A card is drawn from a pack of 52 cards. If A = card is of diamond, B = card is an ace and \(A \cap B = \)card is ace of diamond, then events A and B are

Answers Choices:

Independent

Mutually exclusive

Dependent

Equally likely

Questions 2 of 50

Question:If A and B are two independent events, then A and \(\bar B\) are

Answers Choices:

Not independent

Also independent

Mutually exclusive

None of these

Questions 3 of 50

Question:A coin is tossed and a dice is rolled. The probability that the coin shows the head and the dice shows 6 is

Answers Choices:

\(\frac{1}{8}\)

\(\frac{1}{{12}}\)

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

1

Questions 4 of 50

Question:A coin is tossed twice. The probability of getting head both the times is

Answers Choices:

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

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

\(\frac{3}{4}\)

1

Questions 5 of 50

Question:Two dice are thrown simultaneously. What is the probability of obtaining a multiple of 2 on one of them and a multiple of 3 on the other

Answers Choices:

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

\(\frac{{11}}{{36}}\)

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

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

Questions 6 of 50

Question:A problem of mathematics is given to three students whose chances of solving the problem are 1/3, 1/4 and 1/5 respectively. The probability that the question will be solved is

Answers Choices:

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

\(\frac{3}{4}\)

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

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

Questions 7 of 50

Question:A bag contains 4 white, 5 black and 6 red balls. If a ball is drawn at random, then what is the probability that the drawn ball is either white or red

Answers Choices:

\(\frac{4}{{15}}\)

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

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

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

Questions 8 of 50

Question:A card is drawn at random from a pack of cards. What is the probability that the drawn card is neither a heart nor a king

Answers Choices:

\(\frac{4}{{13}}\)

\(\frac{9}{{13}}\)

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

\(\frac{{13}}{{26}}\)

Questions 9 of 50

Question:The probability of getting head and tail alternately in three throws of a coin (or a throw of three coins), is

Answers Choices:

\(\frac{1}{8}\)

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

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

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

Questions 10 of 50

Question:If A and B are mutually exclusive events, then the value of P (A or B) is

Answers Choices:

0

1

1

None of these

Questions 11 of 50

Question:A bag contains 5 white, 7 red and 8 black balls. If four balls are drawn one by one without replacement, what is the probability that all are white

Answers Choices:

\(\frac{1}{{969}}\)

\(\frac{1}{{380}}\)

\(\frac{5}{{20}}\)

None of these

Questions 12 of 50

Question:The probability of A, B, C solving a problem are \(\frac{1}{3},\,\frac{2}{7},\,\frac{3}{8}\)respectively. If all the three try to solve the problem simultaneously, the probability that exactly one of them will solve it, is

Answers Choices:

\(\frac{{25}}{{168}}\)

\(\frac{{25}}{{56}}\)

\(\frac{{20}}{{168}}\)

\(\frac{{30}}{{168}}\)

Questions 13 of 50

Question:For independent events \({A_1},\,{A_2},\,..........,{A_n},\) \(P({A_i}) = \frac{1}{{i + 1}},\)\(i = 1,\,\,2,\,......,\,\,n.\) Then the probability that none of the event will occur, is

Answers Choices:

\(\frac{n}{{n + 1}}\)

\(\frac{{n - 1}}{{n + 1}}\)

\(\frac{1}{{n + 1}}\)

None of these

Questions 14 of 50

Question:In order to get at least once a head with probability \( \ge 0.9,\) the number of times a coin needs to be tossed is

Answers Choices:

3

4

5

None of these

Questions 15 of 50

Question:A bag contains 30 balls numbered from 1 to 30, one ball is drawn randomly. The probability that number on the ball is multiple of 5 or 7 is

Answers Choices:

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

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

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

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

Questions 16 of 50

Question:A person can kill a bird with probability 3/4. He tries 5 times. What is the probability that he may not kill the bird

Answers Choices:

\(\frac{{243}}{{1024}}\)

\(\frac{{781}}{{1024}}\)

\(\frac{1}{{1024}}\)

\(\frac{{1023}}{{1024}}\)

Questions 17 of 50

Question:In a college, 25% of the boys and 10% of the girls offer Mathematics. The girls constitute 60% of the total number of students. If a student is selected at random and is found to be studying Mathematics, the probability that the student is a girl, is

Answers Choices:

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

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

\(\frac{5}{8}\)

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

Questions 18 of 50

Question:If two dice are thrown simultaneously then probability that 1 comes on first dice is

Answers Choices:

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

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

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

None of these

Questions 19 of 50

Question:A bag contains 3 red and 5 black balls and a second bag contains 6 red and 4 black balls. A ball is drawn from each bag. The probability that one is red and other is black, is

Answers Choices:

\(\frac{3}{{20}}\)

\(\frac{{21}}{{40}}\)

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

None of these

Questions 20 of 50

Question:The probability that a marksman will hit a target is given as 1/5. Then his probability of at least one hit in 10 shots, is

Answers Choices:

\(1 - {\left( {\frac{4}{5}} \right)^{10}}\)

\(\frac{1}{{{5^{10}}}}\)

\(1 - \frac{1}{{{5^{10}}}}\)

None of these

Questions 21 of 50

Question:A bag contains 3 red, 7 white and 4 black balls. If three balls are drawn from the bag, then the probability that all of them are of the same colour is

Answers Choices:

\(\frac{6}{{71}}\)

\(\frac{7}{{81}}\)

\(\frac{{10}}{{91}}\)

None of these

Questions 22 of 50

Question:If four persons are chosen at random from a group of 3 men, 2 women and 4 children. Then the probability that exactly two of them are children, is

Answers Choices:

\(\frac{{10}}{{21}}\)

\(\frac{8}{{63}}\)

\(\frac{5}{{21}}\)

\(\frac{9}{{21}}\)

Questions 23 of 50

Question:A three digit number is formed by using numbers 1, 2, 3 and 4. The probability that the number is divisible by 3, is

Answers Choices:

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

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

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

\(\frac{3}{4}\)

Questions 24 of 50

Question:From a pack of playing cards three cards are drawn simultaneously. The probability that these are one king, one queen and one jack is

Answers Choices:

\(\frac{{64}}{{5525}}\)

\(\frac{{16}}{{5525}}\)

\(\frac{{128}}{{5525}}\)

\(\frac{{64}}{{625}}\)

Questions 25 of 50

Question:A mapping is selected at random from the set of all the mappings of the set \(A = \left\{ {1,\,\,2,\,...,\,n} \right\}\)into itself. The probability that the mapping selected is an injection is

Answers Choices:

\(\frac{1}{{{n^n}}}\)

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

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

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

Questions 26 of 50

Question:A lot consists of 12 good pencils, 6 with minor defects and 2 with major defects. A pencil is choosen at random. The probability that this pencil is not defective is

Answers Choices:

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

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

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

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

Questions 27 of 50

Question:Five digit numbers are formed using the digits 1, 2, 3, 4, 5, 6 and 8. What is the probability that they have even digits at both the ends

Answers Choices:

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

\(\frac{3}{7}\)

\(\frac{4}{7}\)

None of these

Questions 28 of 50

Question:A bag contains 3 red, 4 white and 5 black balls. Three balls are drawn at random. The probability of being their different colours is

Answers Choices:

\(\frac{3}{{11}}\)

\(\frac{2}{{11}}\)

\(\frac{8}{{11}}\)

None of these

Questions 29 of 50

Question:A pack of cards contains 4 aces, 4 kings, 4 queens and 4 jacks. Two cards are drawn at random. The probability that at least one of these is an ace, is

Answers Choices:

\(\frac{9}{{20}}\)

\(\frac{3}{{16}}\)

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

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

Questions 30 of 50

Question:A fair coin is tossed 100 times. The probability of getting tails an odd number of times is

Answers Choices:

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

\(\frac{1}{8}\)

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

None of these

Questions 31 of 50

Question:An event has odds in favour 4 : 5, then the probability that event occurs, is

Answers Choices:

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

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

\(\frac{4}{9}\)

\(\frac{5}{9}\)

Questions 32 of 50

Question:For an event, odds against is 6 : 5. The probability that event does not occur, is

Answers Choices:

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

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

\(\frac{5}{{11}}\)

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

Questions 33 of 50

Question:If A and B are any two events, then the probability that exactly one of them occur is

Answers Choices:

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

\(P\,(A) + P\,(B) - 2P\,(A \cap B)\)

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

\(P\,(A) + P\,(B) - 2P\,(A \cup B)\)

Questions 34 of 50

Question:A coin is tossed twice. If events A and B are defined as :A = head on first toss, \(B = \)head on second toss. Then the probability of \(A \cup B = \)

Answers Choices:

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

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

\(\frac{1}{8}\)

\(\frac{3}{4}\)

Questions 35 of 50

Question:For two given events A and B, \(P\,(A \cap B) = \)

Answers Choices:

Not less than \(P(A) + P\,(B) - 1\)

Not greater than \(P(A) + P(B)\)

Equal to \(P(A) + P(B) - P(A \cup B)\)

All of the above

Questions 36 of 50

Question:\(P(A \cup B) = P(A \cap B)\)if and only if the relation between \(P(A)\) and \(P(B)\) is

Answers Choices:

\(P(A) = P(\bar A)\)

\(P\,(A \cap B) = P(A' \cap B')\)

\(P\,(A) = P\,(B)\)

None of these

Questions 37 of 50

Question:The probabilities of occurrence of two events are respectively 0.21 and 0.49. The probability that both occurs simultaneously is 0.16. Then the probability that none of the two occurs is

Answers Choices:

0.3

0.46

0.14

None of these

Questions 38 of 50

Question:Let A and B be events for which \(P(A) = x\), \(P(B) = y,\)\(P(A \cap B) = z,\) then \(P(\bar A \cap B)\) equals

Answers Choices:

\((1 - x)\,y\)

\(1 - x + \,y\)

\(y - z\)

\(1 - x + y - z\)

Questions 39 of 50

Question:Let S be a set containing n elements and we select 2 subsets A and B of S at random then the probability that \(A \cup B = S\) and \(A \cap B = \varphi \) is

Answers Choices:

\({2^n}\)

\({n^2}\)

1/n

\(1/{2^n}\)

Questions 40 of 50

Question:Let A and B are two events and \(P(A') = 0.3\), \(P(B) = 0.4,\,P(A \cap B') = 0.5\), then \(P(A \cup B')\) is

Answers Choices:

0.5

0.8

1

0.1

Questions 41 of 50

Question:For two events A and B, if \(P(A) = P\left( {\frac{A}{B}} \right) = \frac{1}{4}\) and \(P\,\left( {\frac{B}{A}} \right) = \frac{1}{2},\) then

Answers Choices:

A and B are independent

\(P\,\left( {\frac{{A'}}{B}} \right) = \frac{3}{4}\)

\(P\,\left( {\frac{{B'}}{{A'}}} \right) = \frac{1}{2}\)

All of the above

Questions 42 of 50

Question:If two events A and B are such that \(P({A^c}) = 0.3,\,P(B) = 0.4\) and \(P(A{B^c}) = 0.5,\) then \(P[B/(A \cup {B^c})]\) is equal to

Answers Choices:

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

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

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

None of these

Questions 43 of 50

Question:A bag X contains 2 white and 3 black balls and another bag Y contains 4 white and 2 black balls. One bag is selected at random and a ball is drawn from it. Then the probability for the ball chosen be white is

Answers Choices:

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

\(\frac{7}{{15}}\)

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

\(\frac{{14}}{{15}}\)

Questions 44 of 50

Question:Bag A contains 4 green and 3 red balls and bag B contains 4 red and 3 green balls. One bag is taken at random and a ball is drawn and noted it is green. The probability that it comes bag B

Answers Choices:

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

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

\(\frac{3}{7}\)

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

Questions 45 of 50

Question:A biased coin with probability \(p,\,\,0 < p < 1,\) of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even is \(\frac{2}{5},\) then \(p = \)

Answers Choices:

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

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

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

None of these

Questions 46 of 50

Question:The probability of a bomb hitting a bridge is \(\frac{1}{2}\) and two direct hits are needed to destroy it. The least number of bombs required so that the probability of the bridge beeing destroyed is greater then 0.9, is

Answers Choices:

8

7

6

9

Questions 47 of 50

Question:In a bag there are three tickets numbered 1, 2, 3. A ticket is drawn at random and put back and this is done four times. The probability that the sum of the numbers is even, is

Answers Choices:

\(\frac{{41}}{{81}}\)

\(\frac{{39}}{{81}}\)

\(\frac{{40}}{{81}}\)

None of these

Questions 48 of 50

Question:In tossing 10 coins, the probability of getting exactly 5 heads is

Answers Choices:

\(\frac{9}{{128}}\)

\(\frac{{63}}{{256}}\)

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

\(\frac{{193}}{{256}}\)

Questions 49 of 50

Question:A coin is tossed 10 times. The probability of getting exactly six heads is

Answers Choices:

\(\frac{{512}}{{513}}\)

\(\frac{{105}}{{512}}\)

\(\frac{{100}}{{153}}\)

\({}^{10}{C_6}\)

Questions 50 of 50

Question:If a dice is thrown twice, the probability of occurrence of 4 at least once is

Answers Choices:

\(\frac{{11}}{{36}}\)

\(\frac{7}{{12}}\)

\(\frac{{35}}{{36}}\)

None of these