Total Questions:50 Total Time: 75 Min
Remaining:
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
Independent
Mutually exclusive
Dependent
Equally likely
Question:If A and B are two independent events, then A and \(\bar B\) are
Not independent
Also independent
None of these
Question:A coin is tossed and a dice is rolled. The probability that the coin shows the head and the dice shows 6 is
\(\frac{1}{8}\)
\(\frac{1}{{12}}\)
\(\frac{1}{2}\)
1
Question:A coin is tossed twice. The probability of getting head both the times is
\(\frac{1}{4}\)
\(\frac{3}{4}\)
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
\(\frac{5}{{36}}\)
\(\frac{{11}}{{36}}\)
\(\frac{1}{6}\)
\(\frac{1}{3}\)
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
\(\frac{2}{3}\)
\(\frac{4}{5}\)
\(\frac{3}{5}\)
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
\(\frac{4}{{15}}\)
\(\frac{2}{5}\)
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
\(\frac{4}{{13}}\)
\(\frac{9}{{13}}\)
\(\frac{{13}}{{26}}\)
Question:The probability of getting head and tail alternately in three throws of a coin (or a throw of three coins), is
\(\frac{3}{8}\)
Question:If A and B are mutually exclusive events, then the value of P (A or B) is
0
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
\(\frac{1}{{969}}\)
\(\frac{1}{{380}}\)
\(\frac{5}{{20}}\)
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
\(\frac{{25}}{{168}}\)
\(\frac{{25}}{{56}}\)
\(\frac{{20}}{{168}}\)
\(\frac{{30}}{{168}}\)
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
\(\frac{n}{{n + 1}}\)
\(\frac{{n - 1}}{{n + 1}}\)
\(\frac{1}{{n + 1}}\)
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
3
4
5
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
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
\(\frac{{243}}{{1024}}\)
\(\frac{{781}}{{1024}}\)
\(\frac{1}{{1024}}\)
\(\frac{{1023}}{{1024}}\)
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
\(\frac{5}{8}\)
\(\frac{5}{6}\)
Question:If two dice are thrown simultaneously then probability that 1 comes on first dice is
\(\frac{1}{{36}}\)
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
\(\frac{3}{{20}}\)
\(\frac{{21}}{{40}}\)
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
\(1 - {\left( {\frac{4}{5}} \right)^{10}}\)
\(\frac{1}{{{5^{10}}}}\)
\(1 - \frac{1}{{{5^{10}}}}\)
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
\(\frac{6}{{71}}\)
\(\frac{7}{{81}}\)
\(\frac{{10}}{{91}}\)
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
\(\frac{{10}}{{21}}\)
\(\frac{8}{{63}}\)
\(\frac{5}{{21}}\)
\(\frac{9}{{21}}\)
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
\(\frac{2}{7}\)
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
\(\frac{{64}}{{5525}}\)
\(\frac{{16}}{{5525}}\)
\(\frac{{128}}{{5525}}\)
\(\frac{{64}}{{625}}\)
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
\(\frac{1}{{{n^n}}}\)
\(\frac{1}{{n\,!}}\)
\(\frac{{(n - 1)\,!}}{{{n^{n - 1}}}}\)
\(\frac{{n\,!}}{{{n^{n - 1}}}}\)
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
\(\frac{3}{{10}}\)
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
\(\frac{3}{7}\)
\(\frac{4}{7}\)
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
\(\frac{3}{{11}}\)
\(\frac{2}{{11}}\)
\(\frac{8}{{11}}\)
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
\(\frac{9}{{20}}\)
\(\frac{3}{{16}}\)
\(\frac{1}{9}\)
Question:A fair coin is tossed 100 times. The probability of getting tails an odd number of times is
Question:An event has odds in favour 4 : 5, then the probability that event occurs, is
\(\frac{1}{5}\)
\(\frac{4}{9}\)
\(\frac{5}{9}\)
Question:For an event, odds against is 6 : 5. The probability that event does not occur, is
\(\frac{6}{{11}}\)
\(\frac{5}{{11}}\)
Question:If A and B are any two events, then the probability that exactly one of them occur is
\(P\,(A) + P\,(B) - P\,(A \cap B)\)
\(P\,(A) + P\,(B) - 2P\,(A \cap B)\)
\(P\,(A) + P\,(B) - P\,(A \cup B)\)
\(P\,(A) + P\,(B) - 2P\,(A \cup B)\)
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 \(A \cup B = \)
Question:For two given events A and B, \(P\,(A \cap B) = \)
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
Question:\(P(A \cup B) = P(A \cap B)\)if and only if the relation between \(P(A)\) and \(P(B)\) is
\(P(A) = P(\bar A)\)
\(P\,(A \cap B) = P(A' \cap B')\)
\(P\,(A) = P\,(B)\)
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
0.3
0.46
0.14
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
\((1 - x)\,y\)
\(1 - x + \,y\)
\(y - z\)
\(1 - x + y - z\)
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
\({2^n}\)
\({n^2}\)
1/n
\(1/{2^n}\)
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
0.5
0.8
0.1
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
A and B are independent
\(P\,\left( {\frac{{A'}}{B}} \right) = \frac{3}{4}\)
\(P\,\left( {\frac{{B'}}{{A'}}} \right) = \frac{1}{2}\)
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
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
\(\frac{2}{{15}}\)
\(\frac{7}{{15}}\)
\(\frac{8}{{15}}\)
\(\frac{{14}}{{15}}\)
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
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 \(p = \)
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
8
7
6
9
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
\(\frac{{41}}{{81}}\)
\(\frac{{39}}{{81}}\)
\(\frac{{40}}{{81}}\)
Question:In tossing 10 coins, the probability of getting exactly 5 heads is
\(\frac{9}{{128}}\)
\(\frac{{63}}{{256}}\)
\(\frac{{193}}{{256}}\)
Question:A coin is tossed 10 times. The probability of getting exactly six heads is
\(\frac{{512}}{{513}}\)
\(\frac{{105}}{{512}}\)
\(\frac{{100}}{{153}}\)
\({}^{10}{C_6}\)
Question:If a dice is thrown twice, the probability of occurrence of 4 at least once is
\(\frac{7}{{12}}\)
\(\frac{{35}}{{36}}\)