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?
Responses
A
12
17
12 17
B
5
13
5 13
C
1
20
1 20
D
5
17
B
5
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 available on all tables and the number of seats at round tables.
The total number of seats on the rectangular tables is 6 chairs per table multiplied by the number of rectangular tables, which is 6 chairs * the number of rectangular tables = 6 * 6 = 36 chairs.
The total number of seats on the round tables is 4 chairs per table multiplied by the number of round tables, which is 4 chairs * the number of round tables = 4 * 5 = 20 chairs.
So, the total number of seats available on all tables is 36 + 20 = 56 chairs.
Since the freshman will be randomly assigned a seat number, the probability of being seated at a round table is the number of seats at round tables divided by the total number of seats available on all tables.
Therefore, the probability that the first freshman to arrive will be seated at a round table is 20/56 = 5/14.
The correct answer is B) 5.
To calculate the probability of the first freshman being seated at a round table, we need to determine the total number of chairs available and the number of chairs at round tables.
The total number of chairs can be calculated as follows:
6 chairs per rectangular table x the number of rectangular tables + 4 chairs per round table x the number of round tables.
Therefore, the total number of chairs = (6 chairs x number of rectangular tables) + (4 chairs x number of round tables)
= (6 chairs x 1 rectangular table) + (4 chairs x 5 round tables)
= 6 + 20
= 26 chairs
Since there are 26 chairs in total, and 4 of them are at round tables, the probability of the first freshman being seated at a round table is:
Number of chairs at round tables / Total number of chairs
= 4 / 26
Simplifying this fraction, the probability is:
2 / 13
Hence, the answer is D) 5/17.