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
B 5/13
C1/20
D
5/17
To find the probability that the first freshman to arrive will be seated at a round table, we need to consider the total number of seats available and the number of seats at round tables.
There are 6 rectangular tables with 6 chairs each, so the total number of seats at rectangular tables is 6*6 = 36 seats.
There are 5 round tables with 4 chairs each, so the total number of seats at round tables is 5*4 = 20 seats.
The total number of seats available is 36 + 20 = 56 seats.
Since each chair is randomly numbered starting with 1, there are 56 possible seat choices for the first freshman to arrive.
The probability of the first freshman being seated at a round table is the number of seats at round tables (20) divided by the total number of seats available (56).
Therefore, the probability is 20/56 = 5/14.
However, none of the given response options match this probability exactly. The closest option is B) 5/13, but this is still not correct.
Therefore, the correct answer is None of the above.
To calculate 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 and the number of seats at round tables.
The total number of seats at rectangular tables is 6 chairs per table multiplied by the number of rectangular tables, which is not given.
Let's say the number of rectangular tables is 'n'. Therefore, the total number of seats at rectangular tables is 6n.
The total number of seats at round tables is 4 chairs per table multiplied by the number of round tables, which is given as 5. Therefore, the total number of seats at round tables is 4 * 5 = 20 seats.
Now, the total number of seats available is the sum of the seats at rectangular tables and the seats at round tables: 6n + 20.
Since the chairs are randomly numbered starting from 1, the probability of the first freshman being seated at a round table is the number of seats at round tables divided by the total number of seats available.
Therefore, the probability is 20 / (6n + 20).
However, without knowing the value of 'n', we cannot calculate the exact probability. Thus, the correct answer is (D) 5/17, because we cannot determine the probability with the given information.
To find the probability that the first freshman to arrive will be seated at a round table, we need to calculate the total number of chairs and the number of chairs at the round tables.
Total number of chairs:
There are 6 rectangular tables with 6 chairs each, so the total number of chairs at rectangular tables is 6 * 6 = 36.
There are 5 round tables with 4 chairs each, so the total number of chairs at round tables is 5 * 4 = 20.
Since there are a total of 36 + 20 = 56 chairs, the probability of the first freshman sitting at a round table is the number of chairs at round tables divided by the total number of chairs.
Probability = 20 / 56
Simplifying the fraction gives us:
Probability = 5 / 14
Therefore, the correct answer is D) 5/14.