Suppose that 12 people enter an elevator on the 1st floor of a 24 floor building. Assume that all 12 independently pick a floor (above the first) randomly to get off on. What is the expected number offloors no one gets off on?

∑E(x) = 13.49167 floors

Step-by-step explanation:

The expected number of floors no one get off = ∑E(x) where i is from 0 to 23

and E(x) = ∑xP(x)

here x is the indicator of floor where no one gets off, its value is 0 when  atleast one person get off on its floor and 1 when when no one gets off.

Now,

P(x=1) = (22/23)¹²

P(x=0) = [1-(22/23)¹²]

Now,

E(x) = ∑xP(x) = 0* [1-(22/23)¹²] + 1*(22/23)¹² =0.586594704

For total number of floors where no one gets off

∑E(x) = E(x₁)+E(x₂)+E(x₃)........................+E(x₂₃)

∑E(x) = 23*0.586594704

∑E(x) = 13.49167 floors

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step-by-step explanation: