27. Unbiased Choices A woman brought a complaint of gender discrimination to an eight-member HR committee.

The committee, composed of five females and three males, voted 5–3 in favor of the woman, the five females voting for the woman and the three males against. Has the board been affected by gender bias?

That is, if the vote in favor of the woman was 5–3 and the board members were not biased by gender, what is the probability that the vote would split along gender lines (five females for, three males against)?