the following case occured in Gainsville, Florida. the eight-member Human Relations Advisory Board considered the complaint of a woman who claimed discrimination, based on her gender, on the part of a local surveying company. The board, composed of five women and three men, voted 5-3 in favor of the plainiff, the five women voting for the plainiff and the three men against. The attorney representing the company appealed the board's decision by claiming gender bias on the part of the board members. If the vote in favor of the plainiff was 5-3 and the board members were not biased by gender, what is the probability that the vote would spilt along gender lines (five women for, three men against)?

Question

the following case occured in Gainsville, Florida. the eight-member Human Relations Advisory Board considered the complaint of a woman who claimed discrimination, based on her gender, on the part of a local surveying company. The board, composed of five women and three men, voted 5-3 in favor of the plainiff, the five women voting for the plainiff and the three men against. The attorney representing the company appealed the board's decision by claiming gender bias on the part of the board members. If the vote in favor of the plainiff was 5-3 and the board members were not biased by gender, what is the probability that the vote would spilt along gender lines (five women for, three men against)?

Answer 1

To determine the probability that the vote would split along gender lines (five women for, three men against) if there was no gender bias, we need to consider the total number of possible voting outcomes.

Based on the information provided, there are 5 women and 3 men on the board. So, the total number of ways they can vote can be calculated using the binomial coefficient formula:

C(n, k) = n! / (k! * (n-k)!),

where n is the total number of board members (8) and k is the number of women (5).

C(8, 5) = 8! / (5! * (8-5)!) = 56.

This means that there are 56 possible combinations of votes.

Now, let's calculate the number of combinations that result in a 5-3 split along gender lines (five women for, three men against). In this case, the women need to vote in favor of the plaintiff and the men against.

Considering the 5 women voting for the plaintiff, the number of ways they can vote is given by C(5, 5) = 1.

For the 3 men voting against the plaintiff, the number of ways they can vote is given by C(3, 3) = 1.

Therefore, the number of combinations resulting in a 5-3 split is 1 * 1 = 1.

Finally, the probability is given by the number of favorable outcomes (5-3 split, which is 1) divided by the total number of outcomes (56):

Probability = 1 / 56 ≈ 0.018 or 1.8%.

Answer 2

To calculate the probability that the vote would split along gender lines, given that the board members were not biased by gender, we need to know the total number of possible voting outcomes.

In this case, there are 8 board members, so the total number of possible voting outcomes is the number of ways to choose 5 out of 8. This can be calculated using the combination formula:

C(n, k) = n! / (k!(n-k)!)

where n is the total number of board members and k is the number of members in favor of the plaintiff (5 in this case).

Using this formula, we can calculate:

C(8, 5) = 8! / (5!(8-5)!) = 56

So, there are 56 possible voting outcomes.

Now, let's calculate the number of outcomes where the vote splits along gender lines (five women for, three men against). Since there are 5 women and 3 men, we can calculate:

C(5, 5) * C(3, 3) = 1 * 1 = 1

So, there is only 1 outcome where the vote splits along gender lines.

Finally, we can calculate the probability by dividing the number of outcomes where the vote splits along gender lines by the total number of possible voting outcomes:

Probability = 1 / 56 ≈ 0.018 (or 1.8%)

Therefore, the probability that the vote would split along gender lines (five women for, three men against) is approximately 0.018 or 1.8%.