Example 1  A fair dice is rolled repeatedly. What is the probability that a 6 will be shown before the fourth roll?

Solution:  Suppose X is the random variable representing the number of independent rolling of the dice before a '6' shows up. Clearly X  will be a geometric random variable with

Example 2   In a binary communication system, the probability of bit error is 0.01. If a very large sequence of bits are transmitted, find the probability that the first error occurs after fourth transmission.