In which century the theory of probability was first developed?

• A) 18th century
• B) 17th century
• C) 16th century
• D) 19th century

Find the number of distinct permutations that can be formed using the letters of the word ”BENZENE”

• A) 320
• B) 120
• C) 220
• D) 420

Let S = {1, 2, 3, 4, 5, 6}, A = {1, 3, 5}, B = {2, 4, 6}, then P(A U B) will be --------

• A) 1/2
• B) 1
• C) 2/3
• D) 0

The addition law of probability for two disjoint events A and B is -------

• A) P(A or B) = P (A) + P(B) - P (A and B)
• B) P(A or B) = P (A) + P (B) - P(A) P(B)
• C) P(A or B) = P(A) + P(B) + P(A) P(B)
• D) P(A or B) = P(A) + P(B)

If A and B are disjoint sets then the mathematical representation of inclusion-exclusion principle is …………….

• A) $n(A \cup B) = n(A) + n(B) - n(A \cup B)$
• B) $n(A \cup B) = n(A) + n(B)$
• C) $$n(A \cup B) = n(A) + n(B) - n(A \cap B)$$
• D) None of these

If X and Y are random variables, then E(aX)is equal to

• A) aX
• B) aE(X)
• C) E(aX)
• D) None of these

The expected value E(X) is obtained by multiplying each value of x with its probability and taking the sum.

• A) True
• B) False
• C)
• D)

Find the value of C(n , n)

• A) 0
• B) 1
• C) None of these
• D) n

Which of the followings is the number of distinct permutations that can be formed using the letters of the word BUZZ ?

• A) 8
• B) 4
• C) 12
• D) 24

Let A and B be the mutually exclusive events, then P(A and B) = ?

• A) 1/2
• B) 1
• C) 0
• D) 2/3

0! = ------

• A) 1
• B) -1
• C) None of these
• D) 0

A boy have 3 red and 4 blue balls, What is the probability that a
ball chosen from the boy is blue?

• A) none
• B) 4/7
• C) 1/7
• D) 3/7

An expected value of a random variable is equal to its mean.

• A) True
• B) False
• C)
• D)

If X and Y are random variables, then E(X-Y)is equal to

• A) E(X)+E(Y)
• B) E(X+Y)
• C) E(X)-E(Y)
• D) E(X-Y)

What is the probability of getting a number greater than 3 when a dice is
tossed?

• A) 1/4
• B) 1/2
• C) 1/5
• D) 1/3

If A is any set and U is the universalset then $$n(\,A'\,) = \_\_\_\_\_\_.$$

• A) $$n(U) - n(U \cap \,A)$$
• B) $$n(U) - n(U \cup \,A)$$
• C) $$n(U) + n(U \cap \,A)$$
• D) $$n(U) + n(U \cup \,A)$$

A tree is normally constructed from______.

• A) right
• B) center
• C) right to left
• D) left to right

The event A ∪ B may be written as?

• A) A ∪ B = (A\B)
• B) A ∪ B = (A\B) ∪ B
• C) A ∪ B = (A\B) - B
• D) A ∪ B = (A\B) ∩ B

$P(A \cap B) = P(A).P(A|B)$

• A) True
• B) False
• C)
• D)

A student is to answer five out of nine questions on exams. Find the number of ways that can choose the five questions.

• A) 126
• B) None of these
• C) 316
• D) 216