Answer :
Answer:
The expected number of keys she will try before she opens the door is 4.5.
Step-by-step explanation:
A woman has eight keys on a key ring, one of which fits the door she wants to unlock.
Each of them is equally as likely to be the one to work, which means that this situation is represented by an uniform distribution with lower bound [tex]a = 1[/tex] and upper bound [tex]b = 8[/tex].
Find the expected number of keys she will try before she opens the door.
The expected value of the uniform distribution is given by:
[tex]E = \frac{a + b}{2}[/tex]
Considering [tex]a = 1, b = 8[/tex], as is the case in this exercise:
[tex]E = \frac{1 + 8}{2} = 4.5[/tex]
The expected number of keys she will try before she opens the door is 4.5.
