Suppose that in our league, half of MLB batters have a “true talent” on-base percentage (“OBP” or the probability that a batter gets on base in a plate appearance) of .310 and the other half have a true-talent on-base percentage of .350. In scanning the season-to-date batting statistics, you see that Billy Bases has gotten on base 35 times in 100 plate appearances. Without any additional information about Billy’s performance so far this season, what is the probability that his “true-talent” OBP matches his current OBP of .350?