A point is chosen at random on a line segment of length 12. Find the probability that the ratio of the shorter to the longer segment is less than 3/20.
here let point is at x distance from start.
therefore if x <6
P(X/(12-X) <3/20 ) =P(20X< 36-3X) =P(23X<36) =P(X<36/23) =(36/23)/(12) =3/23
similarly for X>6
P((12-X)/X <3/20) =P(240-20X <3X) =P(X>240/23)= 1-(240/23)/12 =3/23
therefore probability that the ratio of the shorter to the longer segment is less than 3/20 =3/23+3/23 =6/23
A point is chosen at random on a line segment of length 12. Find the probability...
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