In an Auction , two players are bidding. Their bids will be a unknown fraction of their valuations. The valuations come from a uniform distribution $$[0,1] $$
If Player 2 bids $$ v/2 $$ and Player 1 bids $$b1<1/2$$
What is the probability player 1 wins ? Clearly for player 1 to win,players 2 bid has to be less than player 1 bids. $$P(v/2 < b1)$$ $$P(v < 2b1)$$ I follow the question up to this stage. Now it says since its uniformly distributed the probability player 1 wins is $$2b1$$ Im confused how can you just get 2b1 from the inequality ?
Thanks in advance