Question

A legal document is signed with a RSA signature. The probability that a signature sent out by email is intercepted is (.1). Three signatures were sent out by email. Find the probability that at least one signature is intercepted.

Answer 1

Solution:

Given:

p = The probability that a signature sent out by email is intercepted = 0.1

n = Number of signatures were sent out by email = 3

Thus X = Number of signature sent out by email is intercepted follows Binomial distribution with n = 3 and p = 0.1

thus q = 1 - p = 1 - 0.1 = 0.9

We have to find:

the probability that at least one signature is intercepted.

Use formula:

where

thus

thus

thus the probability that at least one signature is intercepted is 0.271