Stacy and Clinton are setting up the community center for a freshman orientation. They set up 8 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 8 rectangular tables with 6 chairs each, so the total number of rectangular chairs is 8 x 6 = <<8*6=48>>48 chairs.
There are also 5 round tables with 4 chairs each, so the total number of round chairs is 5 x 4 = <<5*4=20>>20 chairs.
The total number of chairs in the community center is 48 + 20 = <<48+20=68>>68 chairs.
Since the chairs are randomly numbered and the freshman will be randomly assigned a seat number, the probability that the first freshman to arrive will be seated at a round table is the ratio of the number of round chairs to the total number of chairs, which is 20/68 = <<20/68=0.2941>>0.2941, or 29.41%. Answer: \boxed{0.2941}.
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 total number of round tables.
The total number of seats on rectangular tables is 8 tables * 6 chairs/table = 48 chairs.
The total number of seats on round tables is 5 tables * 4 chairs/table = 20 chairs.
Next, we need to find the total number of seats available for the first freshman to be seated. This is the total number of seats, which is 48 + 20 = 68 seats.
Since the chairs are randomly numbered starting with 1 and the freshman will be randomly assigned a seat number, it doesn't matter which specific seat the freshman sits on.
Therefore, the probability that the first freshman to arrive will be seated at a round table is given by the number of seats at the round tables divided by the total number of seats.
Probability = Number of seats at round tables / Total number of seats
Probability = 20 chairs / 68 chairs
Simplifying the expression, the probability is:
Probability = 20/68 = 0.2941 (rounded to four decimal places)
Therefore, the probability that the first freshman to arrive will be seated at a round table is approximately 0.2941 or 29.41%.