Here's my reasoning......
1st Flip....possible scenarios
( Starting Floor ⇒ Ending Floor )
6 ⇒ 7
6 ⇒ 5
Second Flip ....possible scenarios
7 ⇒ 8
7 ⇒ 6
5 ⇒ 6
5 ⇒ 4
Third flip - possible scenarios
8 ⇒ 9
8 ⇒ 7
6 ⇒ 7 [ this one is no good...being at the 6th floor intially means that she was below the 7th floor on one of the flips....the requirement is being at 7 or higher on all 5 flips ]
6 ⇒ 5
4 ⇒ 5
4 ⇒ 3
Fourth Flip - possible scenarios
9 ⇒ 10 5 ⇒ 6
9 ⇒ 8 5 ⇒ 4
7 ⇒ 8 3 ⇒ 4
7 ⇒ 6 3 ⇒ 2
Last Flip - possible scenarios
10 ⇒ 11 6 ⇒ 7 2 ⇒ 3
10 ⇒ 9 6 ⇒ 5 2 ⇒ 1
8 ⇒ 9 4 ⇒ 5
8 ⇒ 7 4 ⇒ 3
Total possible scenarios = 2 + 4 + 6 + 8 + 10 = 30
Notice, however, that only 11 of these guarantee a floor of 7th or higher on each of 5 flips
Favorable flip 1 outcomes
6 ⇒ 7
Favorable flip 2 outcomes
7 ⇒ 8
Favorable Flip 3 outcomes
8 ⇒ 9
8 ⇒ 7
Favorable Flip 4 outcomes
9 ⇒10
9 ⇒ 8
7 ⇒ 8
Favorable Flip 5 outcomes
10 ⇒ 11
10 ⇒ 9
8 ⇒ 9
8 ⇒ 7
So.......the probability that she is on a floor 7th or higher on each of the 5 flips is
11 / 30
