Professor keeps regurgitating the same answer as the book...it does not make sen

Question

Professor keeps regurgitating the same answer as the book...it does not make sense to me:

During off-peak hours a commuter train has five cars. Suppose a commuter is twice as likely to select the middle car (#3) as to select either adjacent car (#2 or #4), and is twice as likely to select either adjacent car as to select either end car (#1 or #5).

why is p3 = 2p2=2p4, to me the way it is written "a commuter is twice as likely to select middle car p3" why is this not 2 X p3???

Next it says to select either car p2 or p4 not twice p2 or p4???

Explanation / Answer

SEE THE TOTAL SUM OF PROBABILITY OF SELECTION OF ALL CAR WILL BE = 1

NOW IT IS GIVEN THAT  commuter is twice as likely to select the middle car (#3) as to select either adjacent car (#2 or #4), WHICH MEANS CHANCES OG SELECTING 3RD CAR ID TWICE THAT OF 2 AND 4TH

THEREFORE IT WILL BE LIKE THIS

P(X=4) = P(X=3)/4

P(X=2) = P(X=3)/2

ALSO IT IS GIVEN THAT twice as likely to select either adjacent car as to select either end car (#1 or #5).

WHICH WILL BE P(1) = 2P(2) = P(3)/4

P(5) = 2P(4) = P(3)/4

NOW ADD P(1)+P(2)+P(3)+P(4)+P(5) = 1

= P(3)/4+P(3)/2+P(3)+P(3)/2+P(3)/4 = 1

= P(3)= 4/10 = 0.4

HENCE P(2)=P(4) = 0.4/2 = 0.2

HENCE PROBABILITY OF SELECTING P(2) OR P(4) = 0.2+0.2 = 0.4

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