Consider the famiiar game of trying to guess what number will land from a single roll of the die. It a 1 lands. you win $410. Otherwise. you lose $10. The dealer rolls the die and covers the result so that you are not ae to observe the realization of the die. However. your friend catches a glimpse and tells you that it is an 'odd" number on the die providing you with a binary signal realization. By what factor has this signal increased the posterior probability of winning relative to the prior probability of winning (ex-ante relative to the signal realization)? (hint: compute the ratio of the posterior likelihood of winning given the signal realization to the prior likelihood of winning.) [0.5