Math221 – Mathematics for Computer Science S2-2024 Assignment 3

Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

Math221 – Mathematics for Computer Science

S2-2024 Assignment 3

1.      Let n = ℕ, and a, b, c, d = ℤ. Prove that a = b (mod n) if and only if a and bhave the same remainder after being divided by n. (14 marks)

2.         Find the linear combination of gcd for 139 and -191. (14 marks)

3.       In RSA cryptography, if the public key (25, 551), find the private key. (14 marks)

4.       In RSA cryptography, if the public key and private key are (25, 551) and (121, 551) respectively, find the following:

i)       original message (decrypted message) for the cyphertext text 298.

ii)      encrypted message (cyphertext) for the original message 15. (16 marks)

5.         In a group of 100 students, 90 study Mathematics, 80 study Physics, and 5 study none of these subjects. Find the probability that a randomly selected student: (a) studies Mathematics given that he or she studies Physics, and (b) does not study Physics given that he or she studies Mathematics. (14 marks)

6.       In a certain assembly plant, three machines, Machine 1, Machine 2 and Machine 3 make 30%, 45% and  25% respectively of the products. It is known from the quality control data collected from the past that 2%, 3% and 2% of the products made by each machine respectively, are defective. If a product is chosen randomly chosen and found to be defective, what is the probability that it is made by Machine 3? (14 marks)

7.       5 people are to be chosen at random from 5 men and 4 women to form a team. Find the probability that the team contains

(i)         3 men and 2 women,

(ii)       at least 3 men.   (14 marks)