Probability

Question 21

A random bit string of length n is constructed by tossing a fair coin n times and setting a bit to 0 or 1 depending on outcomes head and tail, respectively. The probability that two such randomly generated strings are not identical is

• 1/2ⁿ
• 1 - (1/n)
• (1/n!)
• 1 - (1/2ⁿ)

Question 22

If a fair coin is tossed four times. What is the probability that two heads and two tails will result?

• 3/8
• 1/2
• 5/8
• 2/4

Question 23

In a bunch of 13 T-shirts only one is of Medium size, which is correct fit for the searching person. Each time wrong size is picked, the person throws it away and pick the next T-shirt. What is the probability that the correct size T-shirt can be searched in 8th attempt ?

• 1/1287
• 1/330
• 5/13
• 1/13

Question 24

An examination paper has 150 multiple-choice questions of one mark each, with each question having four choices. Each incorrect answer fetches -0.25 mark. Suppose 1000 students choose all their answers randomly with uniform probability. The sum total of the expected marks obtained by all these students is:

• 0
• 2550
• 7525
• 9375

Question 25

Two n bit binary strings, S1 and S2, are chosen randomly with uniform probability. The probability that the Hamming distance between these strings (the number of bit positions where the two strings differ) is equal to d is

• nCd /2ⁿ
• nCd / ^d
• d/2ⁿ
• 1/2^d

Question 26

A point is randomly selected with uniform probability in the X-Y plane within the rectangle with corners at (0,0), (1,0), (1,2) and (0,2). If p is the length of the position vector of the point, the expected value of p² is

• 2/3
• 1
• 4/3
• 5/3

Question 27

Let P(E) denote the probability of the event E. Given P(A) = 1, P(B) = 1/2, the values of P(A | B) and P(B | A) respectively are

• 1/4, 1/2
• 1/2, 1/14
• 1/2, 1
• 1, 1/2

Question 28

A program consists of two modules executed sequentially. Let f1(t) and f2(t) respectively denote the probability density functions of time taken to execute the two modules. The probability density function of the overall time taken to execute the program is given by :

		 
A) [Tex]f_{1}(t)+f_{2}(t)[/Tex]
B) [Tex]\\int_{0}^{t}f_{1}(x)f_{2}(x)dx[/Tex]
C) [Tex]\\int_{0}^{t}f_{1}(x)f_{2}(t-x)dx[/Tex]
D) [Tex]max\\left \\{ f_{1}(t),f_{2}(t) \\right \\}[/Tex]

• A
• B
• C
• D

Question 29

Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is :

• 1/16
• 1/8
• 7/8
• 15/16

Question 30

Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day?

• 1/7⁷
• 1/7⁶
• 1/2⁷
• 7/2⁷