rectangular tables with 6 chairs each and 5 round tables with 4 chairs each. The chairs are randomly numbered starting with 1 and the freshman will be randomly assigned a seat number.
What is the probability that the first freshman to arrive will be seated at a round table?
There are a total of 6 rectangular tables with 6 chairs each, which gives a total of 6 x 6 = <<6*6=36>>36 chairs at rectangular tables.
There are also a total of 5 round tables with 4 chairs each, which gives a total of 5 x 4 = <<5*4=20>>20 chairs at round tables.
Thus, there are a total of 36 + 20 = <<36+20=56>>56 chairs in the room.
Since the chairs are randomly numbered starting with 1, the probability that the first freshman to arrive will be seated at a round table is equal to the probability that the first chair they choose is at a round table.
The probability that the first chair they choose is at a round table is equal to the number of chairs at round tables, divided by the total number of chairs in the room.
Therefore, the probability is 20/56 = <<20/56=0.357>>0.357.
So the probability that the first freshman to arrive will be seated at a round table is 0.357 or 35.7%. Answer: \boxed{0.357}.
To find the probability that the first freshman will be seated at a round table, we need to calculate the total number of possible seats and the number of seats at round tables.
First, let's find the total number of seats. We have 6 chairs for each rectangular table, so there are 6 * number of rectangular tables = 6 * number of rectangular tables = 6 * 1 = 6 chairs.
We also have 4 chairs for each round table, so there are 4 * number of round tables = 4 * number of round tables = 4 * 5 = 20 chairs.
Now, let's find the number of seats at round tables. We have 5 round tables, and each table has 4 chairs, so the total number of seats at round tables is 5 * 4 = 20 chairs.
The probability that the first freshman will be seated at a round table is the number of seats at round tables divided by the total number of seats:
Probability = Number of seats at round tables / Total number of seats
Probability = 20 / (6 + 20) = 20 / 26 ≈ 0.769 or 76.9%.
Therefore, the probability that the first freshman to arrive will be seated at a round table is approximately 0.769 or 76.9%.
To find the probability that the first freshman to arrive will be seated at a round table, we need to determine the total number of seats and the number of seats at the round tables.
Let's start by calculating the total number of seats. We have 6 chairs each for the rectangular tables, which gives us a total of 6 * 2 = 12 chairs. Additionally, we have 5 round tables with 4 chairs each, which gives us a total of 5 * 4 = 20 chairs.
The total number of seats is now 12 + 20 = 32 chairs.
Next, we need to determine the number of seats at the round tables. Since there are 5 round tables and each table has 4 chairs, we have a total of 5 * 4 = 20 chairs at the round tables.
Finally, to calculate the probability, we divide the number of seats at the round tables by the total number of seats. In this case, the probability is 20/32 = 5/8.
Therefore, the probability that the first freshman to arrive will be seated at a round table is 5/8.