(a) A building has n floors numbered 1,2,...,n, plus a ground floor G. At the ground floor, m people get on the elevator together, and each gets off at a uniformly random one of the n floors (independently of everybody else). What is the expected number of floors the elevator stops at (not counting the ground floor)

The expected number of floors the elevator stops at, not counting the ground floor is =

n*(1-(1-1/n)^m)

Step-by-step explanation:

Here, we want to know the expected number of floors the elevator stops at.

let X1,X2,X3,..Xn are indicator variable for which value =1 if at least one person stops on that floor otherwise value is 0

P(at least one person stops at floor Xj)=1-P(none of m people stops at floor j)

=1-(1-1/n)^m

here total number of floors on elevetor Stops X=X1+X2+X3+...+Xn

hence expected number of floors on elevetor Stops

E(X)=E(X1)+E(X2)+E(X3)...+E(Xn)

=(1-(1-1/n)^m )+(1-(1-1/n)^m )+(1-(1-1/n)^m )+(1-(1-1/n)^m )+ n times

=n*(1-(1-1/n)^m)

answer:

payment just for service  

→

$

87.12

payment for service including tax

→

$

94.09

explanation:

service only with 20% tip  

→

$

72.6

(

1

+

20

100

)

=

$

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the  

service

−−−−−−  

so technically the answer is  

→

$

72.6

(

1

+

20

100

)

=

$

87.12

however, the intention of the question provider may have been that your answer is to be  

$

87.12

(

1

+

8

100

)

=

$

94.09

to 2 decimal places.

'

payment just for service  

→

$

87.12

payment for service including tax

→

$

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge  

.

→

$

72.60

20% tip  

20

100

×

$

72.60

=

$

14.52

−−−−−−  

←

add

$

87.12

tax  

8

100

×

$

87.12

=

$

6.97

−−−−−  

←

add

$

94.09

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