TOPIC: PROBABILITY
1. Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively.
One of the urn is selected at random and a ball is drawn from it. If the ball drawn is black, then the
probability that it is drawn from urn A is: (04.04.24_Shift-1)
1) 2) 3) 4)
2. n a tournament, a team plays 10 matches with probabilities of winning and losing each match as 1/3
and 2/3 respectively. Let x be the number of matches that the team wins, and y be the number of
matches that team loses. If the probability equals _____
(04.04.2024_Shift-2)
3. The coefficients a,b,c in the quadratic equation are chosen from the set .
The probability of this equation having repeated roots is (05.04.24_Shift-1)
1) 2) 3) 4)
4. The coefficients a, b, c in the quadratic equation
2
ax bx c 0 are chosen from the set
{1,2,3,4,5,6,7,8}. The probability of this equation having repeated roots is (05.04.24_Shift-2)
1) 2) 3) 4)
5. The number of wats of getting a sum 16 on throwing a dice four times is _______ (05.04.24_Shift-2)
6. A company has two plants A and B to manufacture motorcycles. 60% motorcycles are manufactured
at plant A and the remaining are manufactured at plant B. 80% of the motorcycles manufactured at
plant A are rated of the standard quality, while 90% of the motorcycles manufactured at plant B are
rated of the standard quality. A motorcycle picked up randomly from the total production is found to
be of the standard quality. If p is the probability that it was manufactured at plant B, then 126p is
(06.02.24_Shift-1)
1) 64 2) 56 3) 54 4) 66
7. If three letters can be posted to any one of the 5 different addresses, then the probability that the three
letters are posted to exactly two addresses is (06.04.24_Shift-2)
(1) (2) (3) (4)
8. Let the sum of two positive integers be 24. If the probability, that their product is not
less than times their greatest possible product, is , where , then
equals (08.04.24_Shift-1)
Page No. 1
A) 9 B) 10 C) 11 D) 8
9. There are three bags and . Bag contains 5 one-rupee coins and 4 fivee-rupee coins; Bag
contains 4 one-rupee coins and 5 five-rupee coins and Bag contains 3 one-rupee coins and 6 five-rupee
coins. A bag is selected at random and a coin drawn from it at random is found to be a one-rupee coin. Then
the probability, that it came from bag is (08.04.24_Shift-2)
1) 2) 3) 4)
10. Let a, b and c denote the outcome of three independent rolls of a fair tetrahedral die, whose four
faces are marked 1, 2, 3, 4. If the probability that ax2 + bx + c = 0 has all real roots is gcd(m,
n) = 1, then m + n is equal to . (09.04.24_Shift-1)
KEY:
1 2 3 4 5 6 7 8 9 10
4 8288 2 2 125 3 3 2 1 19
SOLUTIONS:
1. Urn A contains 7 red, 5 black
Urn B contains 5 red, 7 black
Urn C contains 6 red, 6 black
By Baye’s theorem,
2.
Page No. 2
3. Given quadratic equation is where a,b,c for repeated roots,
must be a perfect square
Corresponding b must lie in set
Probability
4. Given quadratic equation is
ax2 + bx +c = 0 where a,b,c {1,2,3…..8}
For repeated roots,
b2-4ac=0
b2 = 4ac.
ac must be a perfect square
(a,c) {(1,1), (1,4), (2,2), (2,8), (3,3), (4,1), (4,4), (5,5), (6,6), (7,7), (8,2), (8,8)}
Corresponding B must lie in set {1,2,3,….8}
(a,b,c) {(1,2,1) (1,2,4), (2,4,2), (2,8,8), (3,6,3), (4,4,1), (4,8,4), (8,8,2)}
probability = =
Page No. 3
5.
6. P (standard automobile from A) =
P (standard automobile from B) =
Required Probability
P=
So, 126P =
7. We have 3 letters and 5 addresses, where 3 letters are posted to exactly 2 addresses. First, we will
select 2 addresses in ways.
Now, 3 letters can be posted to exactly 2 addresses in 6 ways. (2 + 2 + 2)
8.
Sample space
Integer points on line in shaded region
9. By Baye’s theorem
Page No. 4
Probability (coin drawn from bag y)
10. ax2 + bx + c = 0
for real roots b2 – 4ac 0 …(i)
a, b, c {1, 2, 3, 4} …(ii)
ordered triplet (a, b, c) satisfying (i) and (ii) are
(1, 2, 1), (1, 3, 1), (2, 3, 1), (1, 3, 2), (1, 4, 1), (1, 4,2), (2, 4, 1), (2, 4, 2), (4, 4, 1), (1, 4, 4), (3, 4, 1),
(1,4, 3),
i.e., total 12 favourable outcomes.
Total number of outcomes = 4 x 4 x 4
Required probability
m + n =1
Page No. 5
