-
question_answer1)
If E and F are events with \[P\,(E)\le P\,(F)\] and \[P\,(E\cap F)>0,\] then [IIT 1998]
A)
Occurrence of \[E\Rightarrow \] Occurrence of F done
clear
B)
Occurrence of \[F\Rightarrow \]Occurrence of E done
clear
C)
Non-occurrence of \[E\Rightarrow \] Non-occurrence of F done
clear
D)
None of the above implications holds done
clear
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question_answer2)
A coin is tossed \[m+n\] times, where \[m\ge n.\] The probability of getting at least m consecutive heads is
A)
\[\frac{n+1}{{{2}^{m+1}}}\] done
clear
B)
\[\frac{n+2}{{{2}^{m+1}}}\] done
clear
C)
\[\frac{m+2}{{{2}^{n+1}}}\] done
clear
D)
None of these done
clear
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question_answer3)
An anti-aircraft gun take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. The probability that the gun hits the plane is [CEE 1993; IIT Screening]
A)
0.25 done
clear
B)
0.21 done
clear
C)
0.16 done
clear
D)
0.6976 done
clear
View Solution play_arrow
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question_answer4)
A bag contains a white and b black balls. Two players A and B alternately draw a ball from the bag replacing the ball each time after the draw till one of them draws a white ball and wins the game. A begins the game. If the probability of A winning the game is three times that of B, then the ratio a : b is
A)
1 : 1 done
clear
B)
1 : 2 done
clear
C)
2 : 1 done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer5)
If \[(1+3p)/3,\,\,(1-p)/4\] and \[(1-2p)/2\] are the probabilities of three mutually exclusive events, then the set of all values of p is [IIT 1986; AMU 2002; AIEEE 2003]
A)
\[\frac{1}{3}\le p\le \frac{1}{2}\] done
clear
B)
\[\frac{1}{3}<p<\frac{1}{2}\] done
clear
C)
\[\frac{1}{2}\le p\le \frac{2}{3}\] done
clear
D)
\[\frac{1}{2}<p<\frac{2}{3}\] done
clear
View Solution play_arrow
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question_answer6)
If n positive integers are taken at random and multiplied together, the probability that the last digit of the product is 2, 4, 6 or 8, is
A)
\[\frac{{{4}^{n}}+{{2}^{n}}}{{{5}^{n}}}\] done
clear
B)
\[\frac{{{4}^{n}}\times {{2}^{n}}}{{{5}^{n}}}\] done
clear
C)
\[\frac{{{4}^{n}}-{{2}^{n}}}{{{5}^{n}}}\] done
clear
D)
None of these done
clear
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question_answer7)
An unbiased coin is tossed. If the result is a head, a pair of unbiased dice is rolled and the number obtained by adding the numbers on the two faces is noted. If the result is a tail, a card from a well shuffled pack of eleven cards numbered 2, 3, 4,.......,12 is picked and the number on the card is noted. The probability that the noted number is either 7 or 8, is [IIT 1994]
A)
0.24 done
clear
B)
0.244 done
clear
C)
0.024 done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer8)
If \[P(A)=0.3,\,\,P(B)=0.4,\,\,P(C)=0.8,\,\,P(AB)=0.08,\] \[P(AC)=0.28,\,\,P(ABC)=0.09,\,\,P(A+B+C)\ge 0.75\] and \[P(BC)=x,\] then [IIT 1983]
A)
\[0.23\le x\le 0.48\] done
clear
B)
\[0.32\le x\le 0.84\] done
clear
C)
\[0.25\le x\le 0.73\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer9)
Odds 8 to 5 against a person who is 40 years old living till he is 70 and 4 to 3 against another person now 50 till he will be living 80. Probability that one of them will be alive next 30 years [MNR 1986]
A)
\[\frac{59}{91}\] done
clear
B)
\[\frac{44}{91}\] done
clear
C)
\[\frac{51}{91}\] done
clear
D)
\[\frac{32}{91}\] done
clear
View Solution play_arrow
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question_answer10)
A rifle man is firing at a distant target and has only 10% chance of hitting it. The minimum number of rounds he must fire in order to have 50% chance of hitting it at least once is [Kurukshetra CEE 1998]
A)
7 done
clear
B)
8 done
clear
C)
9 done
clear
D)
6 done
clear
View Solution play_arrow
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question_answer11)
If the integers m and n are chosen at random between 1 and 100, then the probability that a number of the form \[{{7}^{m}}+{{7}^{n}}\] is divisible by 5 equals [IIT 1999]
A)
\[\frac{1}{4}\] done
clear
B)
\[\frac{1}{7}\] done
clear
C)
\[\frac{1}{8}\] done
clear
D)
\[\frac{1}{49}\] done
clear
View Solution play_arrow
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question_answer12)
There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, is a random order till both the faulty machines are identified. Then the probability that only two tests are needed is [IIT 1998]
A)
\[\frac{1}{3}\] done
clear
B)
\[\frac{1}{6}\] done
clear
C)
\[\frac{1}{2}\] done
clear
D)
\[\frac{1}{4}\] done
clear
View Solution play_arrow
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question_answer13)
Two persons A and B take turns in throwing a pair of dice. The first person to through 9 from both dice will be avoided the prize. If A throws first then the probability that B wins the game is [Orissa JEE 2003]
A)
\[\frac{9}{17}\] done
clear
B)
\[\frac{8}{17}\] done
clear
C)
\[\frac{8}{9}\] done
clear
D)
\[\frac{1}{9}\] done
clear
View Solution play_arrow
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question_answer14)
In four schools \[{{B}_{1}},{{B}_{2}},{{B}_{3}},{{B}_{4}}\]the percentage of girls students is 12, 20, 13, 17 respectively. From a school selected at random, one student is picked up at random and it is found that the student is a girl. The probability that the school selected is \[{{B}_{2}},\]is [Pb. CET 2004]
A)
\[\frac{6}{31}\] done
clear
B)
\[\frac{10}{31}\] done
clear
C)
\[\frac{13}{62}\] done
clear
D)
\[\frac{17}{62}\] done
clear
View Solution play_arrow
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question_answer15)
Probability that a student will succeed in IIT entrance test is 0.2 and that he will succeed in Roorkee entrance test is 0.5. If the probability that he will be successful at both the places is 0.3, then the probability that he does not succeed at both the places is
A)
0.4 done
clear
B)
0.3 done
clear
C)
0.2 done
clear
D)
0.6 done
clear
View Solution play_arrow
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question_answer16)
Six boys and six girls sit in a row. What is the probability that the boys and girls sit alternatively [IIT 1979]
A)
\[\frac{1}{462}\] done
clear
B)
\[\frac{1}{924}\] done
clear
C)
\[\frac{1}{2}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer17)
Cards are drawn one by one at random from a well shuffled full pack of 52 cards until two aces are obtained for the first time. If N is the number of cards required to be drawn, then \[{{P}_{r}}\{N=n\},\] where \[2\le n\le 50,\] is [CEE 1993; IIT 1983]
A)
\[\frac{(n-1)\,(52-n)\,(51-n)}{50\times 49\times 17\times 13}\] done
clear
B)
\[\frac{2\,(n-1)\,(52-n)\,(51-n)}{50\times 49\times 17\times 13}\] done
clear
C)
\[\frac{3\,(n-1)\,(52-n)\,(51-n)}{50\times 49\times 17\times 13}\] done
clear
D)
\[\frac{4(n-1)\,(52-n)\,(51-n)}{50\times 49\times 17\times 13}\] done
clear
View Solution play_arrow
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question_answer18)
Let X be a set containing n elements. If two subsets A and B of X are picked at random, the probability that A and B have the same number of elements, is
A)
\[\frac{^{2n}{{C}_{n}}}{{{2}^{2n}}}\] done
clear
B)
\[\frac{1}{^{2n}{{C}_{n}}}\] done
clear
C)
\[\frac{1\,.\,3\,.\,5......(2n-1)}{{{2}^{n}}}\] done
clear
D)
\[\frac{{{3}^{n}}}{{{4}^{n}}}\] done
clear
View Solution play_arrow
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question_answer19)
If three dice are thrown simultaneously, then the probability of getting a score of 7 is [Kurukshetra CEE 1998]
A)
\[\frac{5}{216}\] done
clear
B)
\[\frac{1}{6}\] done
clear
C)
\[\frac{5}{72}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer20)
Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals [IIT 1998]
A)
\[\frac{1}{2}\] done
clear
B)
\[\frac{7}{15}\] done
clear
C)
\[\frac{2}{15}\] done
clear
D)
\[\frac{1}{3}\] done
clear
View Solution play_arrow
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question_answer21)
One of the two events must occur. If the chance of one is 2/3 of the other, then odds in favour of the other are
A)
2 : 3 done
clear
B)
1 : 3 done
clear
C)
3 : 1 done
clear
D)
3 : 2 done
clear
View Solution play_arrow
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question_answer22)
If A and B are two events such that \[P\,(A\cup B)=P\,(A\cap B),\] then the true relation is [IIT 1985]
A)
\[P\,(A)+P\,(B)=0\] done
clear
B)
\[P\,(A)+P\,(B)=P\,(A)\,P\,\left( \frac{B}{A} \right)\] done
clear
C)
\[P\,(A)+P\,(B)=2\,P\,(A)\,P\,\left( \frac{B}{A} \right)\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer23)
The probability of happening an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then the probability of happening neither A nor B is [IIT 1980; DCE 2000]
A)
0.6 done
clear
B)
0.2 done
clear
C)
0.21 done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer24)
If A and B are two events, then the probability of the event that at most one of A, B occurs, is [IIT Screening]
A)
\[P(A'\cap B)+P(A\cap B')+P(A'\cap B')\] done
clear
B)
\[1-P(A\cap B)\] done
clear
C)
\[P(A')+P(B')+P(A\cup B)-1\] done
clear
D)
All of the these done
clear
View Solution play_arrow
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question_answer25)
For any two events A and B in a sample space [IIT 1991]
A)
\[P\,\left( \frac{A}{B} \right)\ge \frac{P(A)+P(B)-1}{P(B)},\,\,P(B)\ne 0\] is always true done
clear
B)
\[P\,(A\cap \bar{B})=P(A)-P(A\cap B)\] does not hold done
clear
C)
\[P\,(A\cup B)=1-P(\bar{A})\,P(\bar{B}),\] if A and B are disjoint done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer26)
Urn A contains 6 red and 4 black balls and urn B contains 4 red and 6 black balls. One ball is drawn at random from urn A and placed in urn B. Then one ball is drawn at random from urn B and placed in urn A. If one ball is now drawn at random from urn A, the probability that it is found to be red, is [IIT 1988]
A)
\[\frac{32}{55}\] done
clear
B)
\[\frac{21}{55}\] done
clear
C)
\[\frac{19}{55}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer27)
If A and B are two events such that \[P(A)=\frac{1}{2}\]and \[P(B)=\frac{2}{3},\] then
A)
\[P\,(A\cup B)\ge \frac{2}{3}\] done
clear
B)
\[\frac{1}{6}\le P(A\cap B)\le \frac{1}{2}\] done
clear
C)
\[\frac{1}{6}\le P({A}'\cap B)\le \frac{1}{2}\] done
clear
D)
All of the above done
clear
View Solution play_arrow
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question_answer28)
The probability that a leap year selected at random contains either 53 Sundays or 53 Mondays, is [Roorkee 1999]
A)
\[\frac{2}{7}\] done
clear
B)
\[\frac{4}{7}\] done
clear
C)
\[\frac{3}{7}\] done
clear
D)
\[\frac{1}{7}\] done
clear
View Solution play_arrow
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question_answer29)
The probabilities that a student passes in Mathematics, Physics and Chemistry are m, p and c respectively. On these subjects, the student has a 75% chance of passing in at least one, a 50% chance of passing in at least two and a 40% chance of passing in exactly two. Which of the following relations are true [IIT 1999]
A)
\[p+m+c=\frac{19}{20}\] done
clear
B)
\[p+m+c=\frac{27}{20}\] done
clear
C)
\[pmc=\frac{1}{10}\] done
clear
D)
\[pmc=\frac{1}{4}\] done
clear
View Solution play_arrow
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question_answer30)
One bag contains 5 white and 4 black balls. Another bag contains 7 white and 9 black balls. A ball is transferred from the first bag to the second and then a ball is drawn from second. The probability that the ball is white, is [DSSE 1987]
A)
\[\frac{8}{17}\] done
clear
B)
\[\frac{40}{153}\] done
clear
C)
\[\frac{5}{9}\] done
clear
D)
\[\frac{4}{9}\] done
clear
View Solution play_arrow
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question_answer31)
Two numbers are selected at random from the numbers 1, 2, ...... n. The probability that the difference between the first and second is not less than m (where 0<m<n), is
A)
\[\frac{(n-m)\,(n-m+1)}{(n-1)}\] done
clear
B)
\[\frac{(n-m)\,(n-m+1)}{2n}\] done
clear
C)
\[\frac{(n-m)\,(n-m-1)}{2n\,(n-1)}\] done
clear
D)
\[\frac{(n-m)\,(n-m+1)}{2n\,(n-1)}\] done
clear
View Solution play_arrow
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question_answer32)
Three groups A, B, C are competing for positions on the Board of Directors of a company. The probabilities of their winning are 0.5, 0.3, 0.2 respectively. If the group A wins, the probability of introducing a new product is 0.7 and the corresponding probabilities for group B and C are 0.6 and 0.5 respectively. The probability that the new product will be introduced, is [Roorkee 1994]
A)
0.18 done
clear
B)
0.35 done
clear
C)
0.10 done
clear
D)
0.63 done
clear
View Solution play_arrow
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question_answer33)
Consider two events A and B such that \[P(A)=\frac{1}{4},\,\,P\left( \frac{B}{A} \right)=\frac{1}{2},\,\,P\left( \frac{A}{B} \right)=\frac{1}{4}.\] For each of the following statements, which is true I. \[P\,({{A}^{c}}/{{B}^{c}})=\frac{3}{4}\] II. The events A and B are mutually exclusive III. \[P(A/B)+P(A/{{B}^{c}})=1\] [AMU 2000]
A)
I only done
clear
B)
I and II done
clear
C)
I and III done
clear
D)
II and III done
clear
View Solution play_arrow
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question_answer34)
A purse contains 4 copper coins and 3 silver coins, the second purse contains 6 copper coins and 2 silver coins. If a coin is drawn out of any purse, then the probability that it is a copper coin is [BIT Ranchi 1991; MNR 1984; UPSEAT 2000]
A)
4/7 done
clear
B)
3/4 done
clear
C)
37/56 done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer35)
An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face values obtained the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, is [IIT 1993; DCE 2000; Roorkee 2000]
A)
16/81 done
clear
B)
1/81 done
clear
C)
80/81 done
clear
D)
65/81 done
clear
View Solution play_arrow
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question_answer36)
India plays two matches each with West Indies and Australia. In any match the probabilities of India getting point 0, 1 and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independents, the probability of India getting at least 7 points is [IIT 1992; Orissa JEE 2004]
A)
0.8750 done
clear
B)
0.0875 done
clear
C)
0.0625 done
clear
D)
0.0250 done
clear
View Solution play_arrow
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question_answer37)
In binomial probability distribution, mean is 3 and standard deviation is \[\frac{3}{2}\]. Then the probability distribution is [AISSE 1979; Pb. CET 2003]
A)
\[{{\left( \frac{3}{4}+\frac{1}{4} \right)}^{12}}\] done
clear
B)
\[{{\left( \frac{1}{4}+\frac{3}{4} \right)}^{12}}\] done
clear
C)
\[{{\left( \frac{1}{4}+\frac{3}{4} \right)}^{9}}\] done
clear
D)
\[{{\left( \frac{3}{4}+\frac{1}{4} \right)}^{9}}\] done
clear
View Solution play_arrow
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question_answer38)
A dice is thrown \[(2n+1)\] times. The probability of getting 1, 3 or 4 at most n times, is
A)
\[\frac{1}{2}\] done
clear
B)
\[\frac{1}{3}\] done
clear
C)
\[\frac{1}{4}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer39)
A box contains 24 identical balls, of which 12 are white and 12 are black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the 4th time on the 7th draw is [IIT Screening 1994]
A)
\[\frac{5}{64}\] done
clear
B)
\[\frac{27}{32}\] done
clear
C)
\[\frac{5}{32}\] done
clear
D)
\[\frac{1}{2}\] done
clear
View Solution play_arrow
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question_answer40)
The chance of an event happening is the square of the chance of a second event but the odds against the first are the cube of the odds against the second. The chances of the events are
A)
\[\frac{1}{9},\,\frac{1}{3}\] done
clear
B)
\[\frac{1}{16},\,\frac{1}{4}\] done
clear
C)
\[\frac{1}{4},\,\frac{1}{2}\] done
clear
D)
None of these done
clear
View Solution play_arrow