Suppose you are conducting a study of gender preferences for participation in raves. (Whether men or women have a preference to participate in rave music/dance events.) You arrive long before the start of the event and make certain that the club is empty. Then you stand outside the club and record your judgment of the gender of the each person who enters. You collect the following data: {M, M, M, F, U, F, M, F, M, F, F, M, M, F, M, M, M, F, M, M, M, F, M, F, F, U, F, U, M, M, M, F, U, F, M, U, F, M, M, M, F, U, F, F, M, M, M, M, M, F, U, M, F, F} (Where: M = male, F = female, U = uncertain gender) The event gets started and you watch to observe the gender of the people as they exit the club. You note that once people start leaving no-one else enters.
a) Given the number of people you have observed entering, what is the probability that by chance you will observe a woman as the first person to exit?
b) What is the probability that the first two people to exit will be women?
c) What is the probability that a couple composed of a man and a person of uncertain gender will exit first? (That is two people in the sequence, a man followed by an uncertain (U)).
d) What is the probability that, by chance alone men will be the first eight people to leave the Rave? Express the value of this probability in words.
e) Would the value you calculated for part d lead you to think that men disliked the rave more than women? Why or why not?