Mathematics - Probability
Exam Duration: 45 Mins Total Questions : 30
A, B, C are three events, such that P(B)=\(\cfrac { 3 }{ 4 } \) ,\(P(A\cap B\cap \overline { C } )=\cfrac { 1 }{ 3 } \) and \(P(\overline { A } \cap B\cap \overline { C } )=\cfrac { 1 }{ 3 } \) then \(P(B\cap C)\) equals
- (a)
\(\cfrac { 1 }{ 12 } \)
- (b)
\(\cfrac { 1 }{ 6 } \)
- (c)
\(\cfrac { 1 }{ 15 } \)
- (d)
\(\cfrac { 1 }{ 9 } \)
If the letters of the word 'MISSISSIPPI' are written down in a row, the probability that no two I's occur together is:
- (a)
\(\cfrac { 1 }{ 3 } \)
- (b)
\(\cfrac { 7 }{ 33 } \)
- (c)
\(\cfrac { 6 }{ 13 } \)
- (d)
NONE OF THESE
A and B are two independent events. The probability that both A and B occur is \(\cfrac { 1 }{ 6 } \) and the probability that neither of them occurs is \(\cfrac { 1 }{ 3 } \). The probability of occurance of A is
- (a)
\(\cfrac { 1 }{ 2 },\cfrac { 1 }{ 3 } \)
- (b)
\(\cfrac { 1 }{ 3 },\cfrac { 1 }{ 4 } \)
- (c)
\(\cfrac { 1 }{ 2 },\cfrac { 1 }{ 4 } \)
- (d)
NONE OF THESE
Let A and B are two independent events, such that P(A)=0.4, P(B)=P and \(P(A\cap B)=0.7\). The value of p for which A and B are independent is
- (a)
\(\cfrac { 1 }{ 3 } \)
- (b)
\(\cfrac { 1 }{ 4 } \)
- (c)
\(\cfrac { 1 }{ 2 } \)
- (d)
\(\cfrac { 1 }{ 5 } \)
If 10% of bolts produced by a machine are defective, then the probability that out of a sample selected at random, of 7 bolts, not more than 1 is defective is
- (a)
\({ (1.6) }^{ 6 }{ (0.9) }^{ 4 }\)
- (b)
\({ (0.9) }^{ 6 }{ (1.6) }^{ }\)
- (c)
\({ (1.6) }^{ 4}{ (0.9) }^{ 6 }\)
- (d)
NONE OF THESE
The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively; then P(X=1), is
- (a)
\(\cfrac { 1 }{ 32 } \)
- (b)
\(\cfrac { 1 }{ 16 } \)
- (c)
\(\cfrac { 1 }{ 8 } \)
- (d)
\(\cfrac { 1 }{ 4 } \)
In a hotly fought battle, the probability of a combatant losing an eye was 70%, an ear 75%, an arm 80% and a leg 85%. The probability of a combatant losing all the four limbs, is not less than
- (a)
40%
- (b)
30%
- (c)
20%
- (d)
10%
The least number of times a fair coin must be tossed so that probability of getting at least head is not less than 0.8 is,
- (a)
3
- (b)
4
- (c)
5
- (d)
6
A bag contains 50 tickets numbered 1, 2, 3,...,49, 50. Five tickets are drawn at random and arranged in ascending order of magnitude as x1<x2<x3<x4<x5; then the probability that x3=30, is
- (a)
\(\cfrac { ^{ 29 }{ C_{ 2 } }\times ^{ 20 }{ C_{ 2 } } }{ ^{ 50 }{ C_{ 5 } } } \)
- (b)
\(\cfrac { ^{ 29 }{ C_{ 2 } }\times ^{ 21 }{ C_{ 2 } } }{ ^{ 50 }{ C_{ 5 } } } \)
- (c)
\(\cfrac { ^{ 30 }{ C_{ 2 } }\times ^{ 20 }{ C_{ 2 } } }{ ^{ 50 }{ C_{ 5 } } } \)
- (d)
NONE OF THESE
A bag contains 3 red and 3 white balls. Two balls are drawn one-by-one. The probability that they are of different colours, is
- (a)
3/10
- (b)
2/5
- (c)
3/5
- (d)
None of these
A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is
- (a)
\(17\over {3^5}\)
- (b)
\(13\over {3^5}\)
- (c)
\(11\over {3^5}\)
- (d)
\(10\over {3^5}\)
A sum of money is rounded off to the nearest rupee, the probability that the rounded off error is atleast ten paise is
- (a)
\(\frac { 1 }{ 100 } \)
- (b)
\(\frac { 9 }{ 100 } \)
- (c)
\(\frac { 49 }{ 100 } \)
- (d)
\(\frac { 81 }{ 100 } \)
Three players A, B, C in this order, cut a pack of cards, and the whole pack is reshuffled after each cut. If the winner is one who first draws a diamond, then C's chance of winning is
- (a)
9/28
- (b)
9/37
- (c)
9/64
- (d)
27/64
Of the 25 questions in a unit, a student has worked out only 20. In a sessional test of that unit, two questions were asked by the teacher. The probability that the student can solve both the questions correctly, is
- (a)
8/25
- (b)
17/25
- (c)
9/10
- (d)
19/30
All the spades are taken out from a pack of cards. From these cards; cards are drawn one by one without replacement till the ace of spades comes. The probability that the ace comes in the 4th draw is
- (a)
1/13
- (b)
12/13
- (c)
4/13
- (d)
none of these
A four digit number (numbered from 0000 to 9999) is said to be lucky, if sum of its first two digits is equal to sum of its last two digits. If a four digit number is picked up at random, the probability that it is lucky number is
- (a)
1.67
- (b)
2.37
- (c)
0.067
- (d)
0.37
If X follows a binomial distribution with parameters n = 8 and p = 1/2, then p \(\left( |x-4|\le 2 \right) \) is equal to
- (a)
121/128
- (b)
119/128
- (c)
117/128
- (d)
115/128
The probabilities of different faces of a biased dice to appear are as follows
| Face number | 1 | 2 | 3 | 4 | 5 | 6 |
| Probability | 0.1 | 0.32 | 0.21 | 0.15 | 0.05 | 0.17 |
The dice is thrown and it is known that either the face number 1 or 2 will appear. Then, the probability of the face number 1 to appear is
- (a)
5/21
- (b)
5/13
- (c)
7/23
- (d)
3/10
A coin is tossed once, then the sample space is
- (a)
{H}
- (b)
{T}
- (c)
{H, T}
- (d)
None of these
Consider the experiment of rolling a die. Let A be the event of 'getting a prime number and B be the event of 'getting an odd number', then
A and B=
- (a)
{1, 2, 3, 5}
- (b)
{1, 2}
- (c)
{3, 5}
- (d)
{5}
If the letters of the word ASSASSIN are written down at random in a row, the probability that no two S's occur together is
- (a)
\(\frac{1}{35}\)
- (b)
\(\frac{1}{21}\)
- (c)
\(\frac{1}{14}\)
- (d)
\(\frac{1}{28}\)
Two cards are drawn successively with replacement from well-shuffled pack of 52 cards. The probability of drawing two face cards is
- (a)
\(\frac{1}{13}\)
- (b)
\(\frac{1}{13}\times \frac{1}{17}\)
- (c)
\(\frac{1}{52}\times \frac{1}{51}\)
- (d)
\(\frac{3}{13}\times \frac{3}{13}\)
Four whole numbers taken at random are multiplied together. What is the chance that the last digit in the product is 1, 3, 7 or 9?
- (a)
\(\frac{16}{625}\)
- (b)
\(\frac{1}{210}\)
- (c)
\(\frac{8}{125}\)
- (d)
\(\frac{4}{25}\)
In a non-leap year, the probability of getting 53 Sundays or 53 Tuesdays is
- (a)
\(\frac{1}{7}\)
- (b)
\(\frac{2}{7}\)
- (c)
\(\frac{3}{7}\)
- (d)
\(\frac{4}{7}\)
From a well-shuffled deck of 52 cards, a card is drawn at random. Find the probability that the card drawn is either red or a king.
- (a)
\(\frac{7}{13}\)
- (b)
\(\frac{6}{13}\)
- (c)
\(\frac{2}{13}\)
- (d)
\(\frac{5}{13}\)
In a town of 6000 people, 1200 are over 50 years old and 2000 are demales. It is known that 30% of the females are over 50 years. What is the probability that a randomly chosen individual from the town is either female or over 50 years?
- (a)
\(\frac{13}{30}\)
- (b)
\(\frac{15}{30}\)
- (c)
\(\frac{15}{31}\)
- (d)
\(\frac{17}{31}\)
Statement-I:A coin is tossed and then a die is rolled only in case a head is shown on the coin. The sample space for the experiment is S = {H1, H2, H3, H4, H5, H6, T} |
Statement -II : 2 boys and 2 girls are in Room X, and 1 boy and 3 girls are in Room Y. Then, the sample space for the experiment in which a room is selected and then a person, is 5 = {XB1, XB2, XG1, XG2, YB3, YG3, YG4, YG5} where B;, denote the boys and Gj, denote the girls.
- (a)
If both Statement-I and Statement-II are true and Statement-II is the correct explanation of Statement -1.
- (b)
If both Statement-I and Statement-II are true but Statement-II is not the correct explanation of Statement -1.
- (c)
If Statement -I is true but Statement-II is false.
- (d)
If Statement-I is false and Statement-II is true.
Statement-I: If A, B, C are three events such that\(P(A)=\frac { 1 }{ 4 } ,P(B)=\frac { 1 }{ 6 } andP(C)=\frac { 2 }{ 3 } \) then events A, B, C are mutually exclusive
Statement-II: If P(A uB\(\cup\)C) = P(A) + P(B) + P(C) then A, B, C are mutually exclusive events.
- (a)
If both Statement-I and Statement-II are true and Statement-II is the correct explanation of Statement -1.
- (b)
If both Statement-I and Statement-II are true but Statement-II is not the correct
explanation of Statement -1. - (c)
If Statement -I is true but Statement-II is false.
- (d)
If Statement-I is false and Statement-II is true.
Statement-I : Events E and F are such that P(not Eor not F) = 0.25, then E and F are not mutually exclusive.
Statement-II: A and B are events such that P(A) = 0.42,P(B) =0.48 andP(A andB) = 0.16 then P(notA), P(not B) and P(A or B) are 0,58, 0.52 and 0.74, respectively .
- (a)
If both Statement-I and Statement-II are true and Statement-II is the correct explanation of Statement -1.
- (b)
If both Statement-I and Statement-II are true but Statement-II is not the correct explanation of Statement -1.
- (c)
If Statement -I is true but Statement-II is false.
- (d)
If Statement-I is false and Statement-II is true.
If the letters of the word ASSASSINATION are arranged at random. Find the probability that
(i) Four S's come consecutively in the word
(ii) Two I's and two N's come together
(iii) All I's are not coming together
(iv) No two A's are coming together
- (a)
(i) (ii) (iii) (iv) \(\frac{2}{143}\) \(\frac{2}{143}\) \(\frac{25}{26}\) \(\frac{15}{26}\) - (b)
(i) (ii) (iii) (iv) \(\frac{25}{26}\) \(\frac{15}{26}\) \(\frac{2}{143}\) \(\frac{2}{143}\) - (c)
(i) (ii) (iii) (iv) \(\frac{15}{26}\) \(\frac{25}{26}\) \(\frac{2}{143}\) \(\frac{2}{143}\) - (d)
(i) (ii) (iii) (iv) \(\frac{2}{143}\) \(\frac{25}{26}\) \(\frac{2}{143}\) \(\frac{15}{26}\)
1654060945.png)
1654060942.png)
1653987551.png)
1653987086.png)
1582095229.jpg)
