DSE 2014 Question

[kangkan]

Mr  A selects X from an uniform distibution [0,1]. Then MR B repeatedly drwars from [0,1] a number Y until Y is greater than X/2.The expected number of draws for Mr b till he reaches his target is

I tried it like this probability of success in any one drwa is 0.75.... Probabilty of getting 1st success in the xth draw is a geometric distribution with p=0.75...but none of the options are tallying..the correct answer apparently is 2ln2..please help

[Amit Goyal]

Solution is attached.