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A network facing coverage problems has bad RxLev. RxQual can be bad at the same time. Sometimes the RxLev can look OK on the street (i.e. from drivetest) but coverage inside the buildings can be po...

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PROBLEM 4: PARKING LOT PROBLEM (3 points possible) Mary and Tom park their cars in an empty parking lot with parking spaces (i.e,

n≥2 consecutive

w here only one car fits in each n spaces in a row, where

space). Mary and Tom pick parking spaces at random. (All pairs of parking spaces are equally likely.) What is the probability that there is at a t most one empty parking space between them? (Express your answer using standard notation..) notation

(4*n-6)/(n*(n-1))

(n−1)⋅(n−2) Answer:

The sample space is

(i, j j)

outcome

Ω={(i, j j):i≠ j,1≤i, j j≤n}

, where

indicates that Mary and Tom parked in slots

i and j ,

respectivel respec tively. y. We apply apply the discrete discrete uniform uniform probabilit probability y law to find the the required requi red probabilit probability. y. We are intereste interested d in the probabili probability ty of the event event

A={(i, j j)∈Ω:|i− j|≤2}. We first find the cardinality of the set of

Ω

Ω is

Ω

. There are

excludes outcomes of the form

n2−n=n(n−1) .

butt sin inc ce n2 pairs (i, j j) , bu

(i,i)

, the the ca card rdin inal alit ity y

If

n≥3 , event A consists of the four lines indicated in the figure

above and contains event

2(n−1)+2(n−2)=4n−6

elements. If

n=2 ,

A contains exactly 2 elements, namely, (1,2) and (2,1) ,