Since she has seven key the probability that the first one will open the door is

if it takes three attempts to open the door,the probability is

if the three attempts would not work
then the probability that the fourth attempt will open the door is

hope this helps
This means that X in the equation equals -1
3/5 i believe. if you take 7 and divide it by 2 its 3.5.
Lim x->1 (x^2+8x-2)
substitute x =1
= 1^2 +8(1)-2
= 1 +8 -2
= 7
So the limit = 7
52/8 is 6.5 on a calculator, hope this helps