Let A be the subset of B, then ------------

• A) P( A ) > P ( B )
• B) P( A ) = P ( B )
• C) P( A ) < P ( B )
• D) P( A ) <= P ( B )

If A and B are two independent events then $P(A \cap B) = ..................$

• A) P(B)
• B) P(A)
• C) 1
• D) $P(A)P(B)$

In how many ways can the letters of the word 'LEADER' be arranged?

• A) 250
• B) 360
• C) 310
• D) None of these

If A and B be events with P(A)=1/3, P(B)=1/4 and P(A intersection B)=1/6, then P(B | A)= ________ .

• A) 1/12
• B) 1/2
• C) 1/24
• D) 2/3

If A and B be events with P(A)=1/3, P(B)=1/4 and P(A intersection B)=1/6, then P(A U B)= ________ .

• A) 2/3
• B) 5/12
• C) 1/2
• D) 1/24

If A and B are disjoint sets then $P(A|B) = .............$

• A) 0
• B) P(A)
• C) P(B)
• D) 1

If k = 10 and n = 2; find the number of ways using k-Selection.

• A) 1
• B) 10
• C) 11
• D) None of these

The number of possible permutations of the letters of the word,"ADDING" having two D’s together

• A) 2!
• B) 3!
• C) 5!
• D) 6!

Let n(U)=100 and n(A)=25, then n(A')=…………….

• A) 75
• B) 55
• C) 65
• D) 100

If X is a discrete random variable and f(x) is the probability of X, then the expected value of this random variable is equal to:

• A) $x + \sum {f(x)}$
• B) $\sum {(x + f(x))}$
• C) $\sum {f(x)}$
• D) $\sum {xf(x)}$

If a die is tossed how many outcomes the sample space of the experiment will have?

• A) 6
• B) 36
• C) 5
• D) 12

If the random variable X denotes the number of heads when three distinct coins are tossed, then X assumes the value

• A) 0,1,2,3
• B) 1,3,3,1
• C) 0,1,2
• D) 1,2,3

A tree diagram is a tool to list all the logical possibilities of a sequence of events where each event can occur in a ____ number of ways.

• A) Infinite
• B) Finite
• C)
• D)

$P(A|B) = \frac{{P(A \cap B)}}{{P(B)}},\,\,\,\,\,where\,\,.............$

• A) $P(B) = 0$
• B) $P(B) > 1$
• C) $P(B) > 0$
• D) $P(B) < 0$

How many different signals each consisting of five flags hung in a vertical line, can be formed from three identical red flags and two identical blue flags?

• A) 10
• B) 120
• C) 40
• D) 20

The sum of probabilities of all outcome is always equal to “0”.

• A) False
• B) True
• C)
• D)

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

• A) Non of these
• B) $n(A \cup B) = n(A) + n(B)$
• C) $$n(A \cup B) = n(A) + n(B) - n(A \cap B)$$
• D) $n(A \cup B) = n(A) + n(B) - n(A \cup B)$

Let A and B be the mutually exclusive events such that P ( A ) = 0.6, P ( B ) = 0.2, then P ( A U B ) = ?

• A) 0.5
• B) 0.7
• C) 0.4
• D) 0.8

If A and B are finite sets then $$n(A \cup \,B) = \_\_\_\_\_\_.$$

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

If X and Y are independent random variables, then E(XY) is equal to __________.

• A) YE(X)
• B) E(XY)
• C) E(X)E(Y)
• D) XE(Y)