1. Two non-negative integers are chosen at random.
The probability that the sum of the square is
divisible by 11 is

a) 9/16

b) 1/121

c) 9/17

d) 2/121

Explanation:

2. A natural number x is choosen at random from the
first 100 natural numbers. The probability that
\[x+\frac{100}{x}>50\]

is

a) 1/10

b) 11/50

c) 11/20

d) 3/20

Explanation:

3. A bag contains (2n + 1) coins. It is known that
n of these coins have a head on both sides, whereas
the remaining (n + 1) coins are fair. A coin is
picked up at random from the bag and tossed. If the probability that the toss results in a head is 31/42,
then n is equal to

a) 10

b) 11

c) 12

d) 13

Explanation:

4. If X and Y are independent binomial variate
B (5, 1/2) and B (7, 1/2), then P (X + Y = 3) is

a) 55/1024

b) 55/4098

c) 55/2048

d) 55/512

Explanation:

5. Suppose \[n\left(\geq 3\right)\] persons are sitting in a row. Two of
them are selected at random. The probability that
they are not together is

a) \[1-\frac{2}{n}\]

b) \[\frac{2}{n-1}\]

c) \[1-\frac{1}{n}\]

d) \[\frac{2}{n}\]

Explanation:

6. A bag contains four tickets marked with numbers
112, 121, 211, 222. One ticket is drawn at random
from the bag. Let \[E_{i}\left(i=1,2,3\right)\] denote the event
that ith digit on the ticket is 2. Then which of the
following is not true

a) \[E_{1}\] and \[E_{2}\] are independent

b) \[E_{2}\] and \[E_{3}\]are independent

c) \[E_{3}\] and \[E_{1}\] are independent

d) \[E_{1},E_{2}, E_{3}\] are independent

Explanation:

7. If the letters of the word PROBABILITY are
written down at random in a row, the probability
that two B's are together is

a) 2/11

b) 10/11

c) 3/11

d) 6/11

Explanation:

8. If four positive integers are taken at random and
multiplied together, then the probability that the
last digit is 1, 3, 7 or 9 is

a) 1/8

b) 2/7

c) 1/625

d) 16/625

Explanation:

9. Two contestants play a game as follows: each is
asked to select a digit from 1 to 9. If the two digits
match they both win a prize. The probability that
they will win a prize in a single trial is

a) 1/8

b) 7/81

c) 1/9

d) 3/11

Explanation: Total number of ways is 81 out of which 9 are favourable

10. A fair coin is tossed 2n times. Probability of getting
more heads than tails is

a) 1/2

b) \[^{2n}C_{n}\left(\frac{1}{2}\right)^{2n}\]

c) \[1-2^{n}C_{n}\left(\frac{1}{2}\right)^{2n}\]

d) \[\frac{1}{2}-^{2n}C_{n}\left(\frac{1}{2}\right)^{2n+1}\]

Explanation: