Bissoy.com
Doctors Medicines MCQs Q&A

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

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 Correct Answer $$\frac{{{}^{\text{n}}{{\text{C}}_{\text{d}}}}}{{{2^{\text{n}}}}}$$

Related Questions

Consider a binary digital communication system with equally likely 0's and 1's. When binary 0 is transmitted the detector input can lie between the levels -0.25V and +0.25V with equal probability: when binary 1 is transmitted, the voltage at the detector can have any value between 0 and 1 V with equal probability. If the detector has a threshold of 0.2 V (i.e., if the received signal is greater than 0.2 V, the bit is taken as 1), the average bit error probability is
Mohan traveled five cities (A, B, C, D and E) starting from home by a car which has a mileage such that the car can travel 10 km in 1 liter petrol. Distance between city A and B is twice the distance between home to city A. Distance between city B and C is thrice the distance between home to city A. Distance between city C and D is 100. Distance between city D and E is 1.5 times than the distance between B and C. Average distance traveled by Mohan was 41 km between five cities. Find how much petrol was needed by Mohan to travel from city B to D.
Two white and two black balls, kept in two bins are arranged in four ways as shown below. In each arrangement, a bin has to be chosen randomly and only one ball needs to be picked randomly from the chosen bin. Which one of the following arrangements has the highest probability for getting a white face picked?
Consider the following statements in respect of slow sand filter and rapid sand filter: 1. The two filters differ in respect of the standards regarding the non-uniformity of the sand used in their filtering media. 2. The two filters do not differ in respect of the effective size of the sand used in them. 3. The two filters differ in respect of their respective under-drainage system. 4. The two filters differ in respect of their respective rate of filtration. Which of the above statements are correct? 
Given below are two quantities named A & B. Based on the given information; you have to determine the relationship between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Quantity A∶ The probability of getting a number which is completely divisible by 6 when the number is chosen from 1 to 30 Quantity B∶ The probability of getting a perfect square number when the number is chosen from 2 to 30
Given below are two quantities named A & B. Based on the given information; you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Quantity A∶ The probability of getting a number completely divisible by 6 when the number is chosen from 1 to 20 Quantity B∶ The probability of getting a perfect square number when the number is chosen from 2 to 30
Given the two strings “cats” and “dogs”. What is the Hamming distance between two strings?
A box contains red, green and blue colored balls. When one ball is drawn randomly from the box, the probability that it is either green or blue is 2/3. Also, the probability that the ball drawn randomly from the box is either red or green is 3/5. When two balls are drawn one after another from the box, the probability that both balls are of green color is 1/15. Find the total number of balls in the box.
A, B, C, D, E, F, G and H are sitting in a row facing north. There are exactly two persons sitting between D and E. A is sitting third from the left end. B, A, C and G are sitting in that order from left to right but no two of them are in adjacent positions. D, F and H are sitting from left to right in that order, but not necessarily in adjacent positions. If H and D interchange their positions and then D and E interchange their positions, who sits second to the right of A?
The following are the two statements relating to the theory of probability. Indicate the statements being correct or incorrect.
Statement I The probability of the joint occurrence of independent events A and B is equal to the probability of event A multiplied by the probability of event B or vice-versa.
Statement II The probability of the joint occurrence of independent event A and dependent event B is equal to the probability of event A multiplied by the conditionalprobability of event B when event A has occurredor vice-versa.