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)?