Probability of Collision in a Hash Table

To understand the probability of collision in a hash table, we need to consider the number of records and the fill factor of the table.

Given Information:
- Number of records in the hash table = 100
- Probability of collision before the table is 10% full

Calculation:
1. Fill Factor:
The fill factor represents the ratio of the number of records in the hash table to the total number of slots in the hash table. It is calculated as:
Fill Factor = (Number of records in the hash table) / (Total number of slots in the hash table)

2. Total Number of Slots:
The total number of slots in a hash table is a fixed value and depends on the hash function and the size of the hash table. However, since we are not given the specific size of the hash table, we will assume it to be 100 (same as the number of records).

3. Number of Slots Occupied:
The number of slots occupied is the number of records in the hash table. In this case, it is given as 100.

4. Fill Factor Calculation:
Fill Factor = 100 / 100 = 1

5. Probability of Collision:
The probability of collision can be calculated using the formula:
Probability of Collision = 1 - (1 - Fill Factor)^(Number of Slots Occupied)

Substituting the values:
Probability of Collision = 1 - (1 - 1)^(100) = 1 - 0^100 = 1 - 0 = 1

Explanation:
The calculated probability of collision is 1, which means that there will always be a collision in the hash table. However, this contradicts the given information that the probability of collision before the table is 10% full. Therefore, there seems to be an error in the given answer of '0.45'.

Please recheck the given answer or provide additional information to accurately calculate the probability of collision.