1. Suppose X ~ B(n, p) and P(X = 3) = P(X = 5). If p >
1/2, then

a) \[ n\leq 7\]

b) n > 8

c) \[n\geq 9\]

d) \[n\geq 10\]

Explanation:

2. In three throw of a pair dice, the probability throwing
doublets not more than twice is

a) 1/6

b) 5/72

c) 215/216

d) 7/128

Explanation:

3. A bag contains 4 brown and 5 white socks. A man
pulls two socks at random without replacement. The
probability that the man gets both the socks of the
same colour is

a) 5/108

b) 1/6

c) 5/18

d) 4/9

Explanation:

4. A is a set containing n elements. Two subsets P
and Q of A are chosen at random. (P and Q may
have elements in common). The probability that
\[P\cup Q\neq A\] is

a) \[\left(3/4\right)^{n}\]

b) 1/4n

c) \[^{n}C_{2}/2^{n}\]

d) \[1-\left(3/4\right)^{n}\]

Explanation:

5. Three of the six vertices of a regular hexagon are
chosen at random. The probability that the triangle
with these vertices is not equilateral is

a) 1/2

b) 1/5

c) 9/10

d) 1/20

Explanation: Find probability of the complement event.

9/10

6. A positive integer is chosen at random. The
probability that the sum of the digits of its square is
39 is

a) 1/39

b) 2/39

c) 1/11

d) 0

Explanation:

7. A lottery sells \[n^{2}\] tickets and declares n prizes. If
a man purchases n tickets, the probability of his
winning at least one prize is

a) \[\left(n^{2}-n\right)!/\left(n^{2}\right)!\]

b) 1/2n

c) \[\left(n-1\right)!^{2}/\left(n^{2}\right)!\]

d) none of these

Explanation:

8. Let x be a non-zero real number. A determinant is
chosen from the set of all determinants of order 2
with entries x or – x only. The probability that the
value of the determinant is non-zero is

a) 3/16

b) 1/4

c) 1/2

d) 1/8

Explanation:

9. A die is rolled three times. The probability of getting a
number larger than the previous number each time is

a) 5/72

b) 5/54

c) 13/216

d) 1/18

Explanation:

10. In a game called “odd man out man out,”
m (m > 2) persons toss a coin to determiane
who will buy refreshments for the entire group.
A person who gets an outcome different from that
of the rest of the members of the group is called the
odd man out. The probability that there is a loser in
any game is

a) 1/2m

b) \[m/2^{m-1}\]

c) 2/m

d) \[1/2^{m-1}\]

Explanation: