Q) Number theory, Cryptography and Probability with Explain the solution

1. Find the inverse of 19 modulo 141 using Euclidian algorithm.

2. What is the original message encrypted using the RSA system with n = 43.59 and e=13 if the encrypted message is 0667 1947 0671? (The inverse of 13 modulo 2458 is 937 = d (decryption exponent). Assume A = 00, B=01, C=02, .

3. What is the conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up tails?