Probability Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. 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
(a)
(b)
(c)
(d)
2. The chance of one event happeing 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 chance of the first event is
Page 2


PART-I (Single Correct MCQs)
1. 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
(a)
(b)
(c)
(d)
2. The chance of one event happeing 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 chance of the first event is
(a)
(b)
(c)
(d)
3. Two numbers x and y are chosen at random (without replacement) from
amongst the numbers 1, 2, 3, .....2004. The probability that  +  is
divisible by 3 is
(a)
(b)
(c)
(d)
4. A card is drawn from a pack of 52 cards. A gambler bets that it is a
spade or an ace. What are the odds against his winning this bet?
(a) 17 : 52
(b) 52 : 17
(c) 9 : 4
(d) 4 : 9
5. If n objects are distributed at random among n persons, the probability
that at least one of them will not get anything is
(a)
(b)
Page 3


PART-I (Single Correct MCQs)
1. 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
(a)
(b)
(c)
(d)
2. The chance of one event happeing 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 chance of the first event is
(a)
(b)
(c)
(d)
3. Two numbers x and y are chosen at random (without replacement) from
amongst the numbers 1, 2, 3, .....2004. The probability that  +  is
divisible by 3 is
(a)
(b)
(c)
(d)
4. A card is drawn from a pack of 52 cards. A gambler bets that it is a
spade or an ace. What are the odds against his winning this bet?
(a) 17 : 52
(b) 52 : 17
(c) 9 : 4
(d) 4 : 9
5. If n objects are distributed at random among n persons, the probability
that at least one of them will not get anything is
(a)
(b)
(c)
(d) None of these
6. If M and N are any two events. The probability, that exactly one of
them occurs, is
(a) P(M) + P(N) – 
(b) P(M) + P(N) + 
(c) P(M) + P(N)
(d) P(M) + P(N) – 2
7. A four digit number is formed by the digits 1, 2, 3, 4 with no repetition.
The probability that the number is odd is :
(a) zero
(b)
(c)
(d) None of these
8. The probability that a leap year will have 53 Friday or53 Saturday, is
(a)
(b)
(c)
(d)
9. If 12 identical balls are to be placed in 3 identical boxes, then  the
probability that one of the boxes contains exactly 3 balls is :
(a)
Page 4


PART-I (Single Correct MCQs)
1. 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
(a)
(b)
(c)
(d)
2. The chance of one event happeing 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 chance of the first event is
(a)
(b)
(c)
(d)
3. Two numbers x and y are chosen at random (without replacement) from
amongst the numbers 1, 2, 3, .....2004. The probability that  +  is
divisible by 3 is
(a)
(b)
(c)
(d)
4. A card is drawn from a pack of 52 cards. A gambler bets that it is a
spade or an ace. What are the odds against his winning this bet?
(a) 17 : 52
(b) 52 : 17
(c) 9 : 4
(d) 4 : 9
5. If n objects are distributed at random among n persons, the probability
that at least one of them will not get anything is
(a)
(b)
(c)
(d) None of these
6. If M and N are any two events. The probability, that exactly one of
them occurs, is
(a) P(M) + P(N) – 
(b) P(M) + P(N) + 
(c) P(M) + P(N)
(d) P(M) + P(N) – 2
7. A four digit number is formed by the digits 1, 2, 3, 4 with no repetition.
The probability that the number is odd is :
(a) zero
(b)
(c)
(d) None of these
8. The probability that a leap year will have 53 Friday or53 Saturday, is
(a)
(b)
(c)
(d)
9. If 12 identical balls are to be placed in 3 identical boxes, then  the
probability that one of the boxes contains exactly 3 balls is :
(a)
(b)
(c)
(d)
10. 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
(a)
(b)
(c)
(d)
11. If A and B are two events such that P (A) =  and  then
which of the following is not correct?
(a)
(b)
(c)
(d)
12. Let A, B, C be three events. If the probability of occurring exactly one
event out of A and B is 1– a, out of B and C is 1– 2a and out of C and A
is 1 – a, and that of occurring three events simultaneously is a
2
, then the
Page 5


PART-I (Single Correct MCQs)
1. 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
(a)
(b)
(c)
(d)
2. The chance of one event happeing 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 chance of the first event is
(a)
(b)
(c)
(d)
3. Two numbers x and y are chosen at random (without replacement) from
amongst the numbers 1, 2, 3, .....2004. The probability that  +  is
divisible by 3 is
(a)
(b)
(c)
(d)
4. A card is drawn from a pack of 52 cards. A gambler bets that it is a
spade or an ace. What are the odds against his winning this bet?
(a) 17 : 52
(b) 52 : 17
(c) 9 : 4
(d) 4 : 9
5. If n objects are distributed at random among n persons, the probability
that at least one of them will not get anything is
(a)
(b)
(c)
(d) None of these
6. If M and N are any two events. The probability, that exactly one of
them occurs, is
(a) P(M) + P(N) – 
(b) P(M) + P(N) + 
(c) P(M) + P(N)
(d) P(M) + P(N) – 2
7. A four digit number is formed by the digits 1, 2, 3, 4 with no repetition.
The probability that the number is odd is :
(a) zero
(b)
(c)
(d) None of these
8. The probability that a leap year will have 53 Friday or53 Saturday, is
(a)
(b)
(c)
(d)
9. If 12 identical balls are to be placed in 3 identical boxes, then  the
probability that one of the boxes contains exactly 3 balls is :
(a)
(b)
(c)
(d)
10. 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
(a)
(b)
(c)
(d)
11. If A and B are two events such that P (A) =  and  then
which of the following is not correct?
(a)
(b)
(c)
(d)
12. Let A, B, C be three events. If the probability of occurring exactly one
event out of A and B is 1– a, out of B and C is 1– 2a and out of C and A
is 1 – a, and that of occurring three events simultaneously is a
2
, then the
probability that at least one out of A, B, C will occur is
(a)
(b)
(c)
(d) None of these
13. If P (A) = P (B) = x and  = 1/3 , then x = ?
(a) 1/2
(b) 1/3
(c) 1/4
(d) 1/6
14. A bag has 13 red, 14 green and 15 white balls, p
1
 is the probability of
drawing exactly 2 white balls when four balls are drawn. Then the
number of balls of each colour are doubled. Let p
2
 be the probability of
drawing 4 white balls when 8 ball are drawn, then
(a) p
1
 = p
2
(b) p
1
 > p
2
(c) p
1
 < p
2
(d) None of these
15. If,  and  
(a)
(b)
(c)
(d)