1. In RSA cryptography, if the public key (25, 551), find the private key. (15 marks) 2. In RSA cryptography, with the public key given and private key found respectively in Q1), find the encrypted message (cyphertext) for the original message encoded as 15. (14 marks) 3. In RSA cryptography, with the public key given and the private key found in Q!). find the encoded numeric code for original message (decrypted message) for the cyphertext text 298. (14 marks) 4. How many even 4-digit numbers greater than 5000 can be formed from the digits 2,4,7,8,9 if no digit can be used more than once? (14 marks) 5. Two digits are to be chosen at random, one after the other, from the ten digits, without repetition, to form a 2-digit number. Let E and E; be the events that the first digit is even and the second digit is even respectively. Express the following probabilities in terms of these events using probability notations and compute them accordingly: both the first and second digits are even (i) (ii) the second digit is odd (iii) one digit is odd 6. (15 marks) 3 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) 2 men and I woman (ii) at least 1 man 7. In a certain assembly plant, three machines, Machine 1, Machine 2 and Machine 3 make 30%, 50% and 20% respectively of the products. It is known from the quality control data collected from the past that 1%, 2% and 3% 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)