Geometry

Question Analysis
This question involves using a tree diagram to calculate the probability of a specific sequence of events in a password - creation context.
The main focus is on correctly identifying the relevant branches in the tree diagram and multiplying the corresponding probabilities to obtain the probability of the desired outcome.

Key Concept Explanation
In a tree diagram representing a series of events, the probability of a particular sequence is found by multiplying the probabilities along the branches that lead to that sequence.
Each branch represents a possible outcome of an event, and the probabilities on the branches are based on the number of available options at each step.

Step - by - Step Solution
1. Calculate the probability of choosing a lowercase letter as the first character:
The probability of choosing a letter as the first character is 13/18.
Given that a letter is chosen, the probability of choosing a lowercase letter is 1/2.
So, the probability of choosing a lowercase letter first is (13/18) × (1/2) = 13/36.
2. The probability of choosing a number as the...