Question 972967
With replacement, I will assume that nobody knows until the end who won.  Her chance is then 1 in 11.  If the key has already been chosen, then her probability is zero, if that fact is made clear at the onset.

Without replacement, the first person has a (1/11) chance.  The woman is sixth, and the five people before her cannot win.  (10/11)*(9/10)*(8/9)*(7/8)*(6/7).  That product is      30240 /55440=0.545
Her probability is 0.545.

Man in seat 9 has the same probability with replacement with the same concerns raised above. It is 1/11.

Continuing with the probabilities, (5/6)*(4/5)(3/4)=60/120.  His probability is (0.545)*(0.5)=0.278.

Yes, you are correct.  I got sloppy and thought 5/9 was the fractional equivalent of 0.545.  It is not, and your answer is 3/11.  Good pick up.