sidagar wrote:

hi brunel..

after going through the solution i got stuck at the last statement : The probability that either x≥2/3x or x≤1/3x is 2/3

how we can conclude probability is 2/3 and not 1/3.Both the options are given in the answer choices

Look at the problem in this way.

Consider a line segment AB (any length)

Put two points on the line segment (say C and D), such that 2*AC=CB and 2*DB=AD

(i.e. the two points divide the line segment into 1:2 ratio)

Now, consider the question that you have to arbitrarily select a point on the segment.

Note carefully here that if you chose a point between A and C, or D and B, then it will satisfy the condition, which is that one line segment is greater than the twice of other.

Next, notice that C and D divide the line segment in a ration of 1/3 (i.e., AC=CD=DB=1/3*AB)

We also know that any point between C and D will not satisfy the condition

Therefore Probability of condition not true will be when the point is chosen between C and D, which is 1/3

Hence, probability of condition being true is 2/3 and answer is D

Hope this helps.