Question 1

# A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P (A ∪ B) is  3/5 0 1 2/5

Solution

C.

1

A = {4, 5, 6} , B = {1, 2, 3, 4} .
Obviously P (A ∪ B) = 1.

Question 2

## If A, B and C are three sets such that A ∩ B = A∩ C and A ∪ B = A ∪ C, then A = B A = C B = C A ∩ B = φ

Solution

C.

B = C

A ∪ B = A ∪ C
⇒ n (A ∪ B) = n(A ∪ C)
⇒ n(A) + n(B) – n(A ∩ B)
= n(A) + n(C) – n(A ∩C)
n(B) = n(C)

Question 3

## If X = {4n - 3n-1 : n ε N} and Y = {9(n-1):n εN}; where N is the set of natural numbers,then X U Y is equal to N Y-X X Y

Solution

D.

Y

We have X = {4n - 3n-1 : n ε N}
X = {0,9,54,243,.....} [put n = 1,2,3....]
Y = {9(n-1):n ε N}
Y = {0,9,18,27,......}[Put n = 1,2,3....]
It is clear that
X ⊂ Y
Therefore, X U Y = Y

Question 4

## Let A and B be two events such that  where  stands for complement of event A. Then events A and B are equally likely and mutually exclusive equally likely but not independent independent but not equally likely mutually exclusive and independent

Solution

C.

independent but not equally likely

Also P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
⇒ P(B) = 5/6 – 3/4 + 1/4 = 1/3
P(A) P(B) = 3/4 – 1/3 = 1/4 = P(A ∩ B)
Hence A and B are independent but not equally likely.
Question 5

## Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is 256 220 219 211

Solution

C.

219

Given, n(A) =2, n(B) = B
The number of subsets of AXB having 3 or more elements,
=