Finding Mr Right

Ginny is going to a speed-dating event to meet ten potential dinner dates for the evening.  The evening starts with a half-hour session in which she meets and has a short “speed date” with ten bachelors for about two minutes each.  Her goal is to select the best one out of the ten.  After each speed-date, she can choose that bachelor to go out with that evening or pass and move to the next bachelor.  She cannot choose any bachelor that she passed on earlier.  Her strategy going into the event is to never choose any of the first three bachelors and then select the first one that is better than the best of the first three thereafter.  In other words, she uses the first three bachelors to “calibrate” the group.  What is the probability that this strategy will result in her going out with the best of the ten?