Probability of Randomly Selecting a Hotel Room Number

In a hotel with room numbers ranging from 101 to 550, a random room number is chosen. What is the probability that the room number starts with 1, 2, or 3 and ends with 4, 5, or 6? How many total rooms are there?

Total Number of Rooms

There are a total of 450 rooms in the hotel, specifically ranging from room 101 to room 550. This can be calculated as follows:

Total rooms 550 - 101 1 450

Rooms Starting with 1, 2, or 3 and Ending with 4, 5, or 6

There are 90 rooms whose numbers start with 1, 2, or 3 and end with 4, 5, or 6. Let's break it down:

The number system can be analyzed as follows:

Hundreds digit: 3 possibilities (1, 2, or 3) Tens digit: 10 possibilities (0-9) Units digit: 3 possibilities (4, 5, or 6)

Therefore, the total number of rooms fitting the criteria is 3 × 10 × 3 90.

Probability Calculation

Given the total number of rooms is 450, and 90 of them meet the specified criteria, the probability is calculated as:

Probability Number of favorable outcomes / Total number of outcomes

Probability 90 / 450 1 / 5 20%

Understanding the Probability

The probability of 1/5 or 20% means that if a random room number is selected, there is a 20% chance that it will start with 1, 2, or 3 and end with 4, 5, or 6.

This probability is significant in managing hotel inventory and customer queries, as it allows hotel staff to efficiently locate specific rooms and provide guests with accurate information regarding their booking.

Conclusion

In a hotel with 450 rooms, the probability that a randomly selected room number starts with 1, 2, or 3 and ends with 4, 5, or 6 is 20%. This understanding is crucial for both hotel management and guests, ensuring a seamless check-in and check-out process.