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.